In active flood hazard mitigation, lateral flow withdrawal is used to reduce the impact of flood waves in rivers. Through emergency side channels, lateral outflow is generated. The optimal outflow controls the flood in such a way that the cost of the created damage is minimized. The flow is governed by a networked system of nonlinear hyperbolic partial differential equations, coupled by algebraic node conditions. Two types of integrals appear in the objective function of the corresponding optimization problem: Boundary integrals (for example, to measure the amount of water that flows out of the system into the floodplain) and distributed integrals.

For the evaluation of the derivative of the objective function, we introduce an adjoint backwards system. For the numerical solution we consider a discretized system with a consistent discretization of the continuous adjoint system, in the sense that the discrete adjoint system yields the derivatives of the discretized objective function. Numerical examples are included.

}, address = {Basel}, author = {Gugat, Martin}, booktitle = {International Series of Numerical Mathematics}, doi = {10.1007/978-3-7643-7721-2_4}, editor = {Karl-Heinz Hoffmann, Günter Leugering, Michael Hintermüller}, faupublication = {yes}, isbn = {978-3-7643-7721-2}, keywords = {St. Venant equations; subcritical states; adjoint system; optimal boundary control; necessary optimality conditions; classical solutions}, note = {UnivIS-Import:2015-04-20:Pub.2007.nat.dma.zentr.optima}, pages = {69-94}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {Control of Coupled Partial Differential Equations}, title = {{Optimal} {Boundary} {Control} in {Flood} {Management}}, url = {http://link.springer.com/chapter/10.1007/978-3-7643-7721-2_4}, volume = {155}, year = {2007} } @article{faucris.110327624, author = {Jahn, Johannes}, faupublication = {yes}, journal = {Mathematical Methods of Operations Research}, note = {UnivIS-Import:2015-03-05:Pub.1991.nat.dma.pama21.specia}, pages = {175-265}, peerreviewed = {Yes}, title = {{Special} {Issue} on {Vector} {Optimization}}, volume = {35}, year = {1991} } @article{faucris.220859888, abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we show that classical stationarity concepts are meaningful for the resulting complementarity-based reformulation of the mixing equations. Further, we investigate in a numerical study the performance of this reformulation compared to a more compact complementarity-based one that does not feature such beneficial regularity properties. All computations are performed on publicly available data of real-world size problem instances from steady-state gas transport.}, author = {Hante, Falk and Schmidt, Martin}, doi = {10.1007/s13675-019-00112-w}, faupublication = {yes}, journal = {EURO Journal on Computational Optimization}, keywords = {Complementarity constraints; Gas transport networks; Inverse parametric quadratic programming; Mixing; MPCC}, note = {CRIS-Team Scopus Importer:2019-06-18}, peerreviewed = {Yes}, title = {{Complementarity}-based nonlinear programming techniques for optimal mixing in gas networks}, year = {2019} } @incollection{faucris.120448064, author = {Jahn, Johannes}, booktitle = {Methods of Operations Research}, faupublication = {yes}, note = {UnivIS-Import:2015-03-05:Pub.1987.nat.dma.pama21.proble}, pages = {51-59}, peerreviewed = {unknown}, title = {{Problems} of {Vector} {Optimization}}, volume = {57}, year = {1987} } @article{faucris.117910364, author = {Leugering, Günter}, doi = {10.1007/BFb0041994}, faupublication = {no}, journal = {Lecture Notes in Control and Information Sciences}, month = {Jan}, pages = {234-252}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {VOLTERRA} {INTEGRODIFFERENTIAL} {EQUATIONS} {IN} {HILBERT}-{SPACES}}, url = {http://link.springer.com/chapter/10.1007/BFb0041994}, volume = {102}, year = {1987} } @misc{faucris.117917184, author = {Elliot, C and Hintermüller, Michael and Leugering, Günter and Sokolowski, Jan}, doi = {10.1080/10556788.2011.614721}, faupublication = {yes}, month = {Jan}, peerreviewed = {automatic}, title = {{Special} issue on advances in shape and topology optimization: theory, numerics and new applications areas - {Foreword}}, url = {http://www.tandfonline.com/doi/full/10.1080/10556788.2011.614721}, year = {2011} } @inproceedings{faucris.121757944, address = {Turnhout}, author = {Gugat, Martin}, booktitle = {Karl der Große und sein Nachwirken: 1200 Jahre Kultur und Wissenschaft in Europa. Band 2: Mathematisches Wissen}, date = {1995-03-19/1995-03-26}, faupublication = {no}, isbn = {2-503-50674-7/hbk}, keywords = {parametric optimization; Lagrange function}, note = {UnivIS-Import:2015-04-16:Pub.1998.nat.dma.lama1.parame}, pages = {471-483}, peerreviewed = {Yes}, publisher = {Brepols}, title = {{Parametric} {Convex} {Optimization}: {One}-{Sided} {Derivatives} of the {Value} {Function} in {Singular} {Parameters}}, venue = {Aachen}, year = {1998} } @book{faucris.118373464, address = {Aachen}, author = {Jahn, Johannes}, faupublication = {yes}, note = {UnivIS-Import:2015-04-02:Pub.2006.nat.dma.pama21.aufgab}, pages = {132}, publisher = {Shaker}, title = {{Aufgabensammlung} zur {Ingenieurmathematik}}, year = {2006} } @inproceedings{faucris.124257144, author = {Rathmann, Wigand and Kaltenbacher, Manfred and Krug, Andreas and Landes, Hermann and Rausch, Martin and Dietz, Peter and Vogel, Frank}, booktitle = {23. CAD-FEM Users' Meeting}, faupublication = {no}, peerreviewed = {No}, publisher = {CAD-FEM GmbH Grafing}, title = {{Numerical} {Optimization} of {Time}-dependent {Electromechanical} {Systems}}, year = {2005} } @article{faucris.122284184, abstract = {We consider refinement of finite element discretizations by splitting nodes along edges. For this process, we derive asymptotic expansions of Galerkin solutions of linear second-order elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for functionals such as the total potential energy, minimization of which decreases the approximation error in the energy norm. Hence, these sensitivities can be used to define indicators for local h-refinement. Our results suggest that this procedure leads to an efficient adaptive refinement method. This presentation is concerned with a model problem in 1d. The extension of this concept to higher dimensions will be the subject of forthcoming publications. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA.}, author = {Leugering, Günter and Friederich, Jan and Steinmann, Paul}, doi = {10.1002/gamm.201210012}, faupublication = {yes}, journal = {GAMM-Mitteilungen}, pages = {175-190}, peerreviewed = {unknown}, title = {{Adaptive} refinement based on asymptotic expansions of finite element solutions for node insertion in 1d}, volume = {35}, year = {2012} } @article{faucris.110564784, abstract = {In this paper we consider a special optimization problem with two objectives which arises in antenna theory. It is shown that this abstract bicriterial optimization problem has at least one solution. Discretized versions of this problem are also discussed, and the relationships between these finite dimensional problems and the infinite dimensional problem are investigated. Moreover, we present numerical results for special parameters using a multiobjective optimization method.}, author = {Jahn, Johannes and Jüschke, A. and Kirsch, A.}, faupublication = {yes}, journal = {Computational Optimization and Applications}, keywords = {Antenna theory; Multiobjective optimization}, note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.pama21.abicri}, pages = {261-276}, peerreviewed = {Yes}, title = {{A} {Bicriterial} {Optimization} {Problem} of {Antenna} {Design}}, volume = {7}, year = {1997} } @article{faucris.112244264, abstract = {We consider the subcritical flow in gas networks consisting of a finite linear sequence of pipes coupled by compressor stations. Such networks are important for the transportation of natural gas over large distances to ensure sustained gas supply. We analyse the system dynamics in terms of Riemann invariants and study stationary solutions as well as classical non-stationary solutions for a given finite time interval. Furthermore, we construct feedback laws to stabilize the system locally around a given stationary state. To do so we use a Lyapunov function and prove exponential decay with respect to the L2 -solutions together with some extra regularity at the masses and then prove exact boundary controllability and velocity-feedback stabilizability, where controls act on both sides of the mass-spring-coupling.}, author = {Leugering, Günter and Li, Tatsien and Wang, Yue}, booktitle = {Springer INdAM Series}, doi = {10.1007/978-3-030-17949-6_8}, faupublication = {yes}, keywords = {Coupled system of quasilinear wave equations; Dynamical boundary condition; Exact boundary controllability; Visoelastic springs}, note = {CRIS-Team Scopus Importer:2019-07-19}, pages = {139-156}, peerreviewed = {unknown}, publisher = {Springer International Publishing}, series = {Springer INdAM Series}, title = {1-d {Wave} {Equations} {Coupled} via {Viscoelastic} {Springs} and {Masses}: {Boundary} {Controllability} of a {Quasilinear} and {Exponential} {Stabilizability} of a {Linear} {Model}}, volume = {32}, year = {2019} } @article{faucris.122945944, abstract = {We consider general, not necessarily convex, optimization problems with inequality constraints. We show that the smoothed penalty algorithm generates a sequence that converges to a stationary point. In particular, we show that the algorithm provides approximations of the multipliers for the inequality constraints. The theoretical analysis is illustrated by numerical examples for optimal control problems with pointwise state constraints and Robin boundary conditions as presented by Grossmann, Kunz, and Meischner [C. Grossmann, H. Kunz, and R. Meischner,

W

},
author = {Leugering, Günter and Nazarov, Sergei and Schury, Fabian and Stingl, Michael},
doi = {10.1137/110823110},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
keywords = {asymptotic analysis; Eshelby theorem; optimization; elastic patch; pointwise error estimates; integral and local cost functionals},
pages = {512-534},
peerreviewed = {Yes},
title = {{The} {Eshelby} {Theorem} and {Application} to the optimization of an {Elastic} {Patch}},
volume = {72},
year = {2012}
}
@article{faucris.119942944,
abstract = {
A vibrating plate is here taken to satisfy the model equation:*u*_{tt} + Δ^{2}u = 0 (where*Δ*^{2}u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:*u*_{v} = 0 and*(Δu)*_{v} = ϕ = control. Thus, the state is the pair [*u, u*_{t}] and controllability means existence of*ϕ* on Σ:= (0,*T*)×*∂Ω* transfering ‘any’*[u, u*_{t}]_{0} to ‘any’*[u, u*_{t}]_{T}. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For large*T* one has such controllability with*∥ϕ∥ = O(T*^{−1/2}). More surprising is that (based on a harmonic analysis estimate [11]) one has controllability for arbitrarily short times (in contrast to the wave equation:*u*_{tt} = Δu) with log*∥ϕ∥ = O(T*^{−1}) as*T*→0. Some related results on minimum time control are also included.

}, author = {Leugering, Günter and Krabs, W. and Seidman, Thomas I.}, doi = {10.1007/BF01442208}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {205-229}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {A} {VIBRATING} {PLATE}}, url = {http://link.springer.com/article/10.1007/BF01442208}, volume = {13}, year = {1985} } @phdthesis{faucris.202429588, abstract = {Numerical topology optimization based on the ersatz material model is very attractive in the research community and industry. Large scale nonlinear problems can be solved efficiently through the availability of appropriate optimizers, often resulting in non-intuitive solutions. However, topology optimization has not yet been established in the design of practical sensors and actuators. To this end we perform a thorough analysis and discussion of two exemplary piezoelectric devices, a single-frequency loudspeaker and a cantilevered energy harvester.

With respect to the loudspeaker a broad range of objective functions is compared and discussed, culminating in a fully coupled piezoelectric-mechanical-acoustic near field topology optimization problem. Piezoelectric strain cancellation and acoustic short circuits need to be balanced with structural resonance in order to obtain close to resonance performance for almost arbitrary target frequencies. Providing appropriate initial designs proved to be essential for robust optimization.

Cantilevered piezoelectric energy harvesters have been subject to various optimization approaches. However these have generally been based on reduced model assumptions. We present topology optimization of a realistic cantilevered energy harvester model. It proved to be necessary to use advanced topology optimization techniques, stress constraints to enforce practically feasible designs and Heaviside filtering for void features size control and for obtaining a black and white design pattern. To the best of our knowledge, this is the first time that dynamic piezoelectric stress constraints have been formulated for topology optimization. The obtained result is mechanism-based and interpretable to manufacture. This appears to be a novel finding in the field of cantilevered piezoelectric energy harvesting design.

Performing numerical experiments, we were surprised to observe pronounced piezoelectric self-penalization, which means optimal black and white solutions without penalizing design interpolation and additional constraints beside box constraints on the design variable. This phenomenon is only rarely and briefly described in the literature. Within this thesis we perform initial heuristic steps in the analysis of the self-penalization phenomenon, which indeed appears in many different topology optimization problems. Once self-penalization is rigorously understood, our vision is to find methods supporting the self-penalizing effect and to obtain solutions potentially closer to the original problem than constrained and penalized ersatz problems. To this end we present oscillation constraints, a feature size control with independent solid and void feature size without enforcing intermediate pseudo material.

2-boundary controls. For some models it is known that even spectral controllability does not hold. Here we show, thereby extending results obtained in Leugering and Schmidt [10], that the general model is approximatively controllable under some reasonable assumptions.}, author = {Leugering, Günter}, doi = {10.1007/BFb0002592}, faupublication = {no}, journal = {Lecture Notes in Control and Information Sciences}, month = {Jan}, pages = {190-201}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {VISCOELASTIC} {SYSTEMS} - {Proceedings} of the {IFIP} {WG} 7.2 {Working} {Conference} {Santiago} de {Compostela}, {Spain}, {July} 6–9, 1987}, url = {http://link.springer.com/chapter/10.1007/BFb0002592}, volume = {114}, year = {1989} } @article{faucris.107401404, abstract = {This paper is concerned with the analysis of equilibrium problems for two-dimensional elastic bodies with thin rigid inclusions and cracks. Inequality-type boundary conditions are imposed at the crack faces providing a mutual non-penetration between the crack faces. A rigid inclusion may have a delamination, thus forming a crack with non-penetration between the opposite faces. We analyze variational and differential problem formulations. Different geometrical situations are considered, in particular, a crack may be parallel to the inclusion as well as the crack may cross the inclusion, and also a deviation of the crack from the rigid inclusion is considered. We obtain a formula for the derivative of the energy functional with respect to the crack length for considering this derivative as a cost functional. An optimal control problem is analyzed to control the crack growth.}, author = {Khludnev, A. M. and Leugering, Günter}, doi = {10.1002/mma.1308}, faupublication = {yes}, journal = {Mathematical Methods in the Applied Sciences}, pages = {1955--1967}, peerreviewed = {Yes}, title = {{On} elastic bodies with thin rigid inclusions and cracks}, volume = {33}, year = {2010} } @article{faucris.119935904, abstract = {For optimal control problems with ordinary differential equations where the L-infinity-norm of the control is minimized, often bang-bang principles hold. For systems that are governed by a hyperbolic partial differential equation, the situation is different: even if a weak form of the bang-bang principle still holds for the wave equation, it implies no restriction on the form of the optimal control. To illustrate that for the Dirichlet boundary control of the wave equation in general not even feasible controls of bang-bang type exist, we examine the states that can be reached by bang-bang-off controls, that is controls that are allowed to attain only three values: Their maximum and minimum values and the value zero. We show that for certain control times, the difference between the initial and the terminal state can only attain a finite number of values. For the problems of optimal exact and approximate boundary control of the wave equation where the L-infinity-norm of the control is minimized, we introduce dual problems and present the weak form of a bang-bang principle, that states that the values of L-infinity-norm minimal controls are constrained by the sign of the dual solutions. Since these dual solutions are in general given as measures, this is no restriction on the form of the control function: the dual solution may have a finite support, and when the dual solution vanishes, the control is allowed to attain all values from the interval between the two extremal control values.}, author = {Gugat, Martin and Leugering, Günter}, doi = {10.1051/cocv:2007044}, faupublication = {yes}, journal = {Esaim-Control Optimisation and Calculus of Variations}, keywords = {optimal control of pdes;optimal boundary control;wave equation;bang-bang;bang-bang-off;dual problem;dual solutions;L-infinity;measures; 49K20; 35L05}, pages = {254-283}, peerreviewed = {Yes}, title = {{L}-infinity-norm minimal control of the wave equation: {On} the weakness of the bang-bang principle}, url = {http://www.esaim-cocv.org/articles/cocv/abs/2008/02/cocv0585/cocv0585.html}, volume = {14}, year = {2008} } @incollection{faucris.106876264, author = {Jahn, Johannes}, booktitle = {Operations Research Verfahren}, faupublication = {no}, note = {UnivIS-Import:2015-03-05:Pub.1979.nat.dma.pama21.zursta}, pages = {209-215}, peerreviewed = {unknown}, title = {{Zur} {Stabilität} von {Regressionskoeffizienten}}, volume = {33}, year = {1979} } @article{faucris.111290564, abstract = {We consider a tree-like network of open channels with outflow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the flow is modelled by the de St. Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in finite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in the class of C

For vibrating strings also, null-controllability by L(p)-controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation.}, author = {Krabs, W. and Leugering, Günter}, doi = {10.1002/mma.1670170202}, faupublication = {no}, journal = {Mathematical Methods in the Applied Sciences}, pages = {77-93}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {ONE}-{DIMENSIONAL} {VIBRATING} {SYSTEMS} {BY} {W}(0)1,{P}-{CONTROLS} {FOR} p∈[2, ∞]}, url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670170202/abstract}, volume = {17}, year = {1994} } @article{faucris.215204958, abstract = {This paper presents a new Lagrange theory of discrete-continuous conic optimization in an infinite dimensional setting. The following questions are answered for discrete-continuous optimization problems: how to define a Lagrange functional, how Karush-Kuhn-Tucker conditions look like, and which duality results can be obtained? This approach is based on new separation theorems for discrete sets, which are also given in this paper. The developed theory is finally applied to problems of discrete-continuous semidefinite and copositive optimization.}, author = {Jahn, Johannes and Knossalla, Martin}, doi = {10.23952/jnva.2.2018.3.07}, faupublication = {yes}, journal = {Journal of Nonlinear and Variational Analysis}, month = {Jan}, note = {CRIS-Team WoS Importer:2019-04-02}, pages = {317-342}, peerreviewed = {Yes}, title = {{LAGRANGE} {THEORY} {OF} {DISCRETE}-{CONTINUOUS} {NONLINEAR} {OPTIMIZATION}}, volume = {2}, year = {2018} } @incollection{faucris.122685684, abstract = {In these notes we want to present some control strategies for dynamic networks of strings and beams in those situations where the classical concepts of exact or approximate controllability fail. This is, in particular, the case for networks containing circuits. Generically, a residual motion settles in such circuits, even if all nodes are subject to controls. In those situations we resort to controls which direct the flux of energy. Using such controls in a network, we are able to steer the entire energy to preassigned parts of the structure. In practice these parts are more massive and can absorb energy more easily than the fragile elements. We also provide numerical evidence for the control strategies discussed in these notes. The material is related to joint work with J.E. Lagnese and E.G.P.G. Schmidt, and is essentially included [14].}, address = {Basel}, author = {Leugering, Günter}, booktitle = {Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena - International Conference in Vorau (Austria), July 18–24, 1993}, doi = {10.1007/978-3-0348-8530-0_17}, editor = {W. Desch; F. Kappel; K. Kunisch}, faupublication = {no}, isbn = {978-3-0348-8530-0}, keywords = {absorbing;directing and nonlinear controls;disappearing solutions;numerical simulation; 39C20; 39B52; 65M06; 65M60}, month = {Jan}, pages = {301-326}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {ISNM International Series of Numerical Mathematics}, title = {{On} feedback controls for dynamic networks of strings and beams and their numerical simulation}, url = {http://link.springer.com/chapter/10.1007/978-3-0348-8530-0_17}, volume = {118}, year = {1994} } @article{faucris.107398324, abstract = {In this contribution the optimal boundary control problem for a first order nonlinear, nonlocal hyperbolic PDE is studied. Motivated by various applications ranging from re-entrant manufacturing systems to particle synthesis processes, we establish the regularity of solutions for W1,p-data. Based on a general L2 tracking type cost functional, the existence, uniqueness, and regularity of the adjoint system in W1,p is derived using the special structure induced from the nonlocal flux function of the state equation. The assumption of W1,p - and not Lp-regularity comes thereby due to the fact that the adjoint equation asks for more regularity to be well defined. This problem is discussed in detail, and we give a solution by defining a special type of cost functional, such that the corresponding optimality system is well defined.}, author = {Gröschel, Michael and Keimer, Alexander and Leugering, Günter and Wang, Zhiqiang}, doi = {10.1137/120873832}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, pages = {2141--2163}, peerreviewed = {Yes}, title = {{Regularity} {Theory} and {Adjoint}-{Based} {Optimality} {Conditions} for a {Nonlinear} {Transport} {Equation} with {Nonlocal} {Velocity}}, volume = {52}, year = {2014} } @article{faucris.122573044, abstract = {This paper considers dynamical systems under feedback with control actions limited to switching. The authors wish to understand the closed-loop systems as approximating multi-scale problems in which the implementation of switching merely acts on a fast scale. Such hybrid dynamical systems are extensively studied in the literature, but not much so far for feedback with partial state observation. This becomes in particular relevant when the dynamical systems are governed by partial differential equations. The authors introduce an augmented BV setting which permits recognition of certain fast scale effects and give a corresponding well-posedness result for observations with such minimal regularity. As an application for this setting, the authors show existence of solutions for systems of semilinear hyperbolic equations under such feedback with pointwise observations.}, author = {Hante, Falk and Leugering, Günter and Seidman, Thomas I.}, doi = {10.1007/s11424-010-0140-0}, faupublication = {yes}, journal = {Journal of Systems Science & Complexity}, pages = {456--466}, peerreviewed = {Yes}, title = {{An} augmented {BV} setting for feedback switching control}, volume = {23}, year = {2010} } @article{faucris.111644544, author = {Knossalla, Martin}, faupublication = {yes}, journal = {Journal of Nonlinear and Variational Analysis}, pages = {265-279}, peerreviewed = {Yes}, title = {{Concepts} on generalized epsilon-subdifferentials for minimizing locally {Lipschitz} continuous functions}, url = {http://jnva.biemdas.com/archives/404}, year = {2017} } @article{faucris.118531644, abstract = {We investigate the occurrence of self-penalization in topology optimization problems for piezoceramicmechanical composites. Our main goal is to give physical interpretations for this phenomenon, i.e., to study the question why for various problems intermediate material values are not optimal in the absence of explicit penalization of the pseudo densities. In order to investigate this effect numerical experiments for several static and/or dynamic actuator and sensor objective functions are performed and their respective results are compared. The objective functions are mean transduction, displacement, sound power, electric potential, electric energy, energy conversion and electric power.}, author = {Wein, Fabian and Kaltenbacher, Manfred and Kaltenbacher, Barbara and Leugering, Günter and Bänsch, Eberhard and Schury, Fabian}, doi = {10.1007/s00158-010-0570-2}, faupublication = {yes}, journal = {Structural and Multidisciplinary Optimization}, pages = {405-417}, peerreviewed = {Yes}, title = {{On} the effect of self-penalization of piezoelectric composites in topology optimization}, volume = {43}, year = {2011} } @article{faucris.119552224, abstract = {We present an asymptotic approach to find optimal rotations of orthotropic material inclusions inside an isotropic linear elastic matrix. We compute approximate optimal solutions with respect to compliance and a stress based cost functional. We validate the local and global quality of the candidate solutions by means of finite element based parametric optimization algorithms. In particular, we devise a lower bound algorithm based on the free material optimization approach. Several numerical experiments are performed for different traction scenario}, author = {Schury, Fabian and Greifenstein, Jannis and Leugering, Günter and Stingl, Michael}, doi = {10.1007/s11081-014-9262-x}, faupublication = {yes}, journal = {Optimization and Engineering}, pages = {225-246}, peerreviewed = {Yes}, title = {{On} the efficient solution of a patch problem with multiple elliptic inclusions}, volume = {16}, year = {2015} } @incollection{faucris.122069024, address = {Oberwolfach}, author = {Leugering, Günter and Kocvara, Michal and Stingl, Michael}, booktitle = {Optimal Control of Coupled Systems of PDE}, doi = {10.4171/OWR/2008/13}, editor = {Karl Kunisch, Günter Leugering, Jürgen Sprekels and Fredi Tröltzsch}, faupublication = {yes}, pages = {647-649}, peerreviewed = {unknown}, publisher = {European Mathematical Society Publishing House}, series = {Oberwolfach Reports}, title = {{A} {New} {Method} for the {Solution} of {Multi}-{Disciplinary} {Free} {Material} {Optimization} {Problems}}, volume = {13}, year = {2008} } @article{faucris.111889844, abstract = {We consider a finite string that is fixed at one end and subject to a feedback control at the other end which is allowed to move. We show that the behaviour is similar to the situation where both ends are fixed: As long as the movement is not too fast, the energy decays exponentially and for a certain parameter in the feedback law it vanishes in finite time. We consider movements of the boundary that are continuously differentiable with a derivative whose absolute value is smaller than the wave speed. We solve a problem of worst-case optimal feedback control, where the parameter in the feedback law is chosen such that the worst-case L p -norm of the space derivative at the fixed end of the string is minimized (p ∈ 1, ∞)). We consider the worst case both with respect to the initial conditions and with respect to the boundary movement. It turns out that the parameter for which the energy vanishes in finite time is optimal in this sense for all p. © The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.}, author = {Gugat, Martin}, doi = {10.1093/imamci/dnm014}, faupublication = {yes}, journal = {IMA Journal of Mathematical Control and Information}, keywords = {Feedback; Moving boundary; Optimal boundary control; Optimal control of PDEs; PDE constrained optimization; Wave equation}, note = {UnivIS-Import:2015-03-09:Pub.2008.nat.dma.zentr.optima_5}, pages = {111-121}, peerreviewed = {Yes}, title = {{Optimal} boundary feedback stabilization of a string with moving boundary}, url = {http://imamci.oxfordjournals.org/cgi/content/abstract/dnm014?ijkey=sCu0noGNy5dtzdd&keytype=ref}, volume = {25}, year = {2008} } @article{faucris.110144804, abstract = {We consider elliptic problems on graphs under given loads and bilateral contact conditions. We ask the question: which graph is best suited to sustain the loads and the constraints. More precisely, given a cost function we may look at a multiple node of the graph with edge degree q and ask as to whether that node should be resolved into a number of nodes of edge degree less than q, in order to decrease the cost. With this question in mind, we are looking into the sensitivity analysis of a graph carrying a second order elliptic equation with respect to changing its topology by releasing nodes with high edge degree or including an edge. With the machinery at hand developed here, we are in the position to define the topological gradient of an elliptic problem on a graph.}, author = {Leugering, Günter and Sokolowski, Jan}, faupublication = {yes}, journal = {Control and Cybernetics}, keywords = {differential equations on metric graphs;obstacles;topology optimization;asymptotic analysis}, month = {Jan}, pages = {971-997}, peerreviewed = {Yes}, title = {{Topological} sensitivity analysis for elliptic problems on graphs}, url = {https://hal.archives-ouvertes.fr/hal-00261861/}, volume = {37}, year = {2008} } @article{faucris.110644424, abstract = {The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of weak subgradients of set-valued maps is proved, and a sufficient optimality condition of set-valued optimization problems is obtained in terms of weak subgradients.}, author = {Jahn, Johannes and Chen, G.Y.}, faupublication = {yes}, journal = {Mathematical Methods of Operations Research}, keywords = {Generalized contingent epiderivative; Optimality conditions; Set-valued optimization; Subgradient}, note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.pama21.optima}, pages = {187-200}, peerreviewed = {Yes}, title = {{Optimality} {Conditions} for {Set}-{Valued} {Optimization} {Problems}}, volume = {48}, year = {1998} } @misc{faucris.118869344, abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we show that classical stationarity concepts are meaningful for the resulting complementarity-based reformulation of the mixing equations. Further, we investigate in a numerical study the performance of this reformulation compared to a more compact complementarity-based one that does not feature such beneficial regularity properties. All computations are performed on publicly available data of real-world size problem instances from steady-state gas transport.}, author = {Hante, Falk and Schmidt, Martin}, faupublication = {yes}, keywords = {Gas transport networks, Mixing, Inverse parametric quadratic programming, Complementarity constraints, MPCC}, peerreviewed = {automatic}, title = {{Complementarity}-{Based} {Nonlinear} {Programming} {Techniques} for {Optimal} {Mixing} in {Gas} {Networks}}, url = {http://www.optimization-online.org/DB_HTML/2017/09/6198.html}, year = {2017} } @article{faucris.223557645, abstract = {An example by Bastin and Coron illustrates that the boundary stabilization of 1-d hyperbolic systems with certain source terms is only possible if the length of the space interval is sufficiently small. We show that related phenomena also occur for networks of vibrating strings that are governed by the wave equation with a certain source term. It turns out that for a tree of strings with Neumann velocity feedback control at one boundary node and a homogeneous Dirichlet boundary condition at at least one boundary node and homogeneous Dirichlet or Neumann conditions at the other boundary nodes, boundary feedback stabilization is not possible if one of the strings is sufficiently long. However, if the number of strings in the tree is sufficiently large, also for arbitrarily short strings for certain parameters in the source term stabilization is not possible. The wave equation with source term that we consider is equivalent to a certain 2 ×2 system. For the examples that illustrate the limits of stabilizability, the matrix of the source term is not positive definite. However if the system parameters are chosen in such a way that the matrix is positive semi-definite, the tree of strings can be stabilized exponentially fast by the boundary feedback control for arbitrary long space intervals.}, author = {Gugat, Martin and Gerster, Stephan}, doi = {10.1016/j.sysconle.2019.104494}, faupublication = {yes}, journal = {Systems & Control Letters}, keywords = {Limits of stabilizability; Neumann feedback; Source terms; Stabilization; String networks}, note = {CRIS-Team Scopus Importer:2019-08-02}, peerreviewed = {Yes}, title = {{On} the limits of stabilizability for networks of strings}, volume = {131}, year = {2019} } @book{faucris.118439244, abstract = {This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.}, address = {Basel}, doi = {10.1007/978-3-0348-0133-1}, edition = {1}, editor = {Leugering, Günter and Engell, Sebastian and Griewank, Andreas and Hinze, Michael and Rannacher, Rolf and Schulz, Volker and Ulbrich, Michael and Ulbrich, Stefan}, faupublication = {yes}, isbn = {978-3-0348-0132-4}, note = {UnivIS-Import:2015-05-08:Pub.2012.nat.dma.lama1.wellpo}, publisher = {Birkhäuser}, series = {ISNM}, title = {{Constrained} {Optimization} and {Optimal} {Control} for {Partial} {Differential} {Equations}}, url = {http://www.springer.com/de/book/9783034801324}, volume = {160}, year = {2012} } @book{faucris.123698784, abstract = {We consider optimal control problems for elliptic systems under control constraints on networked domains. In particular, we study such systems in a format that allows for applications in problems including membranes and Reissner-Mindlin plates on multi-link-domains, called networks. We first provide the models, derive first order optimality conditions in terms of variational equations and inequalities for a control-constrained linear-quadratic optimal control problem, and then introduce a non-overlapping iterative domain decomposition method, which is based on Robin-type interface updates at multiple joints (edges). We prove convergence of the iteration and derive a posteriori error estimates with respect to the iteration across the interfaces.}, author = {Leugering, Günter}, doi = {10.1007/978-3-540-75199-1_10}, faupublication = {yes}, isbn = {9783540751984}, pages = {119-130}, peerreviewed = {unknown}, title = {{Domain} decomposition of constrained optimal control problems for 2d elliptic system on networked domains: convergence and a posteriori error estimates}, volume = {60}, year = {2008} } @incollection{faucris.117209224, abstract = {We present topology optimization of piezoelectric loudspeakers using the SIMP method and topology gradient based methods along with analytical and numerical results.}, address = {Basel}, author = {Bänsch, Eberhard and Kaltenbacher, Manfred and Leugering, Günter and Schury, Fabian and Wein, Fabian}, booktitle = {Constrained Optimization and Optimal Control for Partial Differential Equations}, doi = {10.1007/978-3-0348-0133-1_26}, editor = {Günter Leugering, Sebastian Engell, Andreas Griewank, Michael Hinze, Rolf Rannacher, Volker Schulz, Michael Ulbrich, Stefan Ulbrich,}, faupublication = {yes}, isbn = {978-3-0348-0132-4}, keywords = {Topology optimization; piezoelectricity; loudspeakers}, pages = {501-519}, peerreviewed = {unknown}, publisher = {Birkhäuser/ Springer Basel AG}, series = {International Series of Numerical Mathematics}, title = {{Optimization} of electro-mechanical smart structures}, volume = {160}, year = {2012} } @incollection{faucris.122007864, abstract = {This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave propagation through heterogenous layers. The motivation is provided by the demand for a better understanding of meta-materials and their possible construction. We stress the analogies between the mathematical treatment of phononic, photonic and elastic meta-materials. Moreover, we treat the cloaking problem in more detail from an analytical and simulation oriented point of view. The novelty in the approach presented here is with the interlinked homogenization- and optimization procedur}, author = {Leugering, Günter and Rohan, Eduard and Seifrt, Frantiek}, booktitle = {Wave Propagation in Periodic Media}, doi = {10.2174/978160805150211001010197}, editor = {Matthias Ehrhardt}, faupublication = {yes}, note = {EAM Import::2019-03-12}, pages = {197-226}, peerreviewed = {unknown}, publisher = {Bentham Science}, series = {Progress in Computational Physics}, title = {{Modeling} of {Metamaterials} in {Wave} {Propagation}}, volume = {1}, year = {2010} } @article{faucris.117906844, abstract = {We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and its solution can be used as suboptimal controls for the original problem.}, author = {Kogut, Peter I. and Leugering, Günter}, doi = {10.1051/cocv:2008037}, faupublication = {yes}, journal = {Esaim-Control Optimisation and Calculus of Variations}, keywords = {Optimal control; homogenization; elliptic equation; periodic graph; 35B27; 35J25; 49J20; 93C20}, pages = {471-498}, peerreviewed = {Yes}, title = {{HOMOGENIZATION} {OF} {CONSTRAINED} {OPTIMAL} {CONTROL} {PROBLEMS} {FOR} {ONE}-{DIMENSIONAL} {ELLIPTIC} {EQUATIONS} {ON} {PERIODIC} {GRAPHS}}, url = {http://www.esaim-cocv.org/articles/cocv/abs/2009/02/cocv0505/cocv0505.html}, volume = {15}, year = {2009} } @inproceedings{faucris.121306504, abstract = {This paper aims at identifying appropriate bottom anti-reflective coatings (BARCs) for double patterning techniques such as Litho-Freeze-Litho-Etch (LFLE). A short introduction into the employed optimization methodology, including variables, figures of merit, models and optimization algorithms is given. A study on the impact of a refractive index modulation caused by the first lithographic step is presented. Several optimization surveys taking the index modulation into account are set forth, and the results are discussed. In addition to optimization procedures aiming at optimizing one litho step at a time, a co-optimization study for both litho steps is proposed. Finally, two multi-objective optimization procedures that allow for a post-optimization exploration and selection of optimum solutions are presented. Numerous solutions are discussed in terms of their anti-reflectance behavior and their manufacturing feasibility. © 2010 SPIE.}, author = {Jahn, Johannes and Erdmann, Andreas and Fühner, Tim and Liu, S. and Shao, F. and Barenbaum, A.}, booktitle = {Proceedings of the SPIE}, date = {2010-02-23/2010-02-25}, doi = {10.1117/12.846441}, faupublication = {yes}, keywords = {bottom anti-reflective coating (BARC); double patterning; lithography simulation; waferstack optimization}, note = {UnivIS-Import:2015-04-16:Pub.2010.nat.dma.pama21.topogr}, pages = {76403C}, peerreviewed = {unknown}, publisher = {SPIE}, title = {{Topography}-aware {BARC} optimization for double patterning}, venue = {San Jose}, volume = {7640}, year = {2010} } @incollection{faucris.118332544, address = {München}, author = {Jahn, Johannes}, booktitle = {Ausgewählte Operations Research Software in FORTRAN}, editor = {H. Späth}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1979.nat.dma.pama21.lsungn}, pages = {30-50}, peerreviewed = {unknown}, publisher = {Oldenbourg}, title = {{Lösung} nichtlinearer {Optimierungsprobleme} mit {Nebenbedingungen}}, year = {1979} } @article{faucris.117325824, abstract = {

We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T, by minimizing an objective functional that is the convex sum of the L^{2}-norm of the control and of a boundary Neumann tracking term.

We provide an explicit solution of this optimal control problem, showing that if the weight of the tracking term is positive, then the optimal control action is concentrated at the beginning and at the end of the time interval, and in-between it decays exponentially. We show that the optimal control can actually be written in that case as the sum of an exponentially decaying term and of an exponentially increasing term. This implies that, if the time T is large, then the optimal trajectory approximately consists of three arcs, where the first and the third short-time arcs are transient arcs, and in the middle arc the optimal control and the corresponding state are exponentially close to 0. This is an example of a turnpike phenomenon for a problem of optimal boundary control. If T=+∞ (infinite time horizon problem), then only the exponentially decaying component of the control remains, and the norms of the optimal control action and of the optimal state decay exponentially in time. In contrast to this situation, if the weight of the tracking term is zero and only the control cost is minimized, then the optimal control is distributed uniformly along the whole interval [0,T] and coincides with the control given by the Hilbert Uniqueness Method.

In addition, we establish a similarity theorem stating that, for every T>0, there exists an appropriate weight λ<1 for which the optimal solutions of the corresponding finite horizon optimal control problem and of the infinite horizon optimal control problem coincide along the first part of the time interval [0,2]. We also discuss the turnpike phenomenon from the perspective of a general framework with a strongly continuous semi-group.

}, author = {Gugat, Martin and Trelat, Emmanuel and ZuaZua, Enrique}, doi = {10.1016/j.sysconle.2016.02.001}, faupublication = {yes}, journal = {Systems & Control Letters}, keywords = {Vibrating string; Neumann boundary control; Turnpike phenomenon; Exponential stability; Energy decay; Exact control; Infinite horizon optimal control; Similarity theorem; Receding horizon}, pages = {61-70}, peerreviewed = {Yes}, title = {{Optimal} {Neumann} control for the {1D} wave equation: {Finite} horizon, infinite horizon, boundary tracking terms and the turnpike property}, volume = {90}, year = {2016} } @inproceedings{faucris.122844744, author = {Gugat, Martin and Tucsnak, Marius and Sigalotti, Mario}, booktitle = {Proceedings of the 9th European Control Conference, Kos, Greece, 2007.}, date = {2007-07-02/2007-07-05}, faupublication = {yes}, note = {UnivIS-Import:2015-04-16:Pub.2007.nat.dma.zentr.robust}, pages = {-}, title = {{Robustness} analysis for the boundary control of the string equation}, url = {http://www.iecn.u-nancy.fr/~sigalott/doc/string.pdf}, venue = {Kos}, year = {2007} } @incollection{faucris.107023664, address = {München}, author = {Jahn, Johannes and Dupre, R. and Huckert, K.}, booktitle = {Ausgewählte Operations Research Software in FORTRAN}, editor = {H. Späth}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1979.nat.dma.pama21.lsungl}, pages = {9-29}, peerreviewed = {unknown}, publisher = {Oldenbourg}, title = {{Lösung} linearer {Vektormaximumprobleme} durch das {STEM}-{Verfahren}}, year = {1979} } @article{faucris.117788044, abstract = {We derive error estimates for finite element discretizations of phase field models that describe phase transitions in nonisothermal mixtures. Special attention is paid to the applicability of the result for a large class of models with nonlinear constitutive relations and to an approach that avoids an exponential dependence of the constants in the error estimate on the approximation parameter that models the thickness of the diffuse phase transition region. The main assumptions on the model are a convexity condition for a function that can be interpreted as the negative local part of the entropy of the system, a suitable regularity of the exact solutions, and a spectrum estimate for the operator of the Allen-Cahn equation. The spectrum estimate is crucial to avoid the exponential dependence of error constants on the approximation parameters in the model. This is done by a technique introduced in [X. Feng and A. Prohl, Math. Comp., 73 (2004), pp. 541-567] for phase transitions of pure materials with linear constitutive relations. © 2010 Society for Industrial and Applied Mathematic}, author = {Eck, Christof and Jadamba, Baasansuren and Knabner, Peter}, doi = {10.1137/050637984}, faupublication = {yes}, journal = {SIAM Journal on Numerical Analysis}, keywords = {A priori error estimate; Finite element method; Phase field model; Thermodynamically consistent model}, pages = {4429-4445}, peerreviewed = {Yes}, title = {{Error} estimates for a finite element discretization of a phase field model for mixtures}, url = {https://www1.am.uni-erlangen.de/research/publications/Jahr_2010/2010_EckJadambaKn_ErrorEstimatesForFiniteElementDiscreOfAPhaseFieldModelForMix}, volume = {47}, year = {2010} } @article{faucris.226679834, abstract = {This paper is devoted to describing the asymptotic behavior of a structure consisting of thin elastic planar beams coupled at flexible joints. As the thickness of the beams tends to zero, we establish classical 1-D beam equations for each individual structural element and transmission conditions across the joints.}, author = {Leugering, Günter and Nazarov, S. A. and Slutskij, A. S.}, doi = {10.1002/zamm.201700192}, faupublication = {yes}, journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik}, keywords = {00-xx; asymptotic analysis; plane systems of beams; thin elastic junctions}, month = {Jan}, note = {CRIS-Team Scopus Importer:2019-09-17}, peerreviewed = {Yes}, title = {{The} asymptotic analysis of a junction of two elastic beams}, volume = {99}, year = {2019} } @article{faucris.120144024, abstract = {There are several studies of the boundary controllability of quasi-linear hyperbolic systems where it is assumed that the eigenvalues of the system matrix do not change their signs during the controlled process.
In this paper we consider the flow through a frictionless horizontal rectangular channel that is governed by de St. Venant equations and show that the state can be controlled in finite time from a stationary initial state to a given stationary terminal state in such a way that during this transition, the state stays in the class of C ^{2} norm of the controls is solved explicitly in the sense that controls that are successful and minimize at the same time the objective function are determined as functions of the initial state. Due to the complementarity condition that appears in the optimal control problem, it is non-convex and the optimal control is in general not uniquely determined. To allow for technical constraints it is important to avoid an accumulation of switching points at so-called Zeno-points. We give examples that illustrate how switching regimes of practical value can be obtained. © 2008 WILEY-VCH Verlag GmbH & Co. KGaA.},
author = {Gugat, Martin},
doi = {10.1002/zamm.200700154},
faupublication = {yes},
journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik},
keywords = {MPEC; Optimal boundary control; PDE constrained optimization; Switching control; Wave equation},
note = {UnivIS-Import:2015-03-09:Pub.2008.nat.dma.zentr.optima},
pages = {283-305},
peerreviewed = {Yes},
title = {{Optimal} switching boundary control of a string to rest in finite time},
url = {http://www3.interscience.wiley.com/cgi-bin/abstract/117946700/ABSTRACT},
volume = {88},
year = {2008}
}
@article{faucris.214606914,
abstract = {Consider a star-shaped network of strings. Each string is governed by the wave equation. At each boundary node of the network there is a player that performs Dirichlet boundary control action and in this way influences the system state. At the central node, the states are coupled by algebraic conditions in such a way that the energy is conserved. We consider the corresponding antagonistic game where each player minimizes a certain quadratic objective function that is given by the sum of a control cost and a tracking term for the final state. We prove that under suitable assumptions a unique Nash equilibrium exists and give an explicit representation of the equilibrium strategies.},
author = {Gugat, Martin and Steffensen, Sonja},
doi = {10.1051/cocv/2017082},
faupublication = {yes},
journal = {Esaim-Control Optimisation and Calculus of Variations},
note = {CRIS-Team WoS Importer:2019-03-26},
pages = {1789-1813},
peerreviewed = {Yes},
title = {{DYNAMIC} {BOUNDARY} {CONTROL} {GAMES} {WITH} {NETWORKS} {OF} {STRINGS}},
volume = {24},
year = {2018}
}
@incollection{faucris.111139424,
abstract = {We consider optimal control problems for the flow of gas or fresh water in pipe networks as well as drainage or sewer systems in open canals. The equations of motion are taken to be represented by the nonlinear isothermal Euler gas equations, the water hammer equations, or the St. Venant equations for flow. We formulate model hierarchies and derive an abstract model for such network flow problems including pipes, junctions, and controllable elements such as valves, weirs, pumps, as well as compressors. We use the abstract model to give an overview of the known results and challenges concerning equilibria, well-posedness, controllability, and optimal control. A major challenge concerning the optimization is to deal with switching on-off states that are inherent to controllable devices in such applications combined with continuous simulation and optimization of the gas flow. We formulate the corresponding mixed-integer nonlinear optimal control problems and outline a decomposition approach as a solution technique.},
address = {Singapore},
author = {Hante, Falk and Leugering, Günter and Martin, Alexander and Schewe, Lars and Schmidt, Martin},
booktitle = {Industrial Mathematics and Complex Systems: Emerging Mathematical Models, Methods and Algorithms},
doi = {10.1007/978-981-10-3758-0_5},
editor = {Manchanda, Pammy; Lozi, René; Siddiqi, Abul Hasan},
faupublication = {yes},
isbn = {978-981-10-3758-0},
keywords = {Networks, pipes, canals, Euler and St. Venant equations, hierarchy of models, domain decomposition, controllability, optimal control.},
pages = {77-122},
peerreviewed = {unknown},
publisher = {Springer Singapore},
series = {Industrial and Applied Mathematics},
title = {{Challenges} in {Optimal} {Control} {Problems} for {Gas} and {Fluid} {Flow} in {Networks} of {Pipes} and {Canals}: {From} {Modeling} to {Industrial} {Applications}},
url = {https://opus4.kobv.de/opus4-trr154/files/121/isiam-paper.pdf},
year = {2017}
}
@article{faucris.123271104,
abstract = {It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio v(ss) = -1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio v(LE) approximate to -0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios v(SS) of the skeletal structure and v(LE) of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.},
author = {Mitschke, Holger and Schwerdtfeger, Jan and Schury, Fabian and Stingl, Michael and Körner, Carolin and Singer, Robert and Robins, Vanessa and Mecke, Klaus and Schröder-Turk, Gerd},
doi = {10.1002/adma.201100268},
faupublication = {yes},
journal = {Advanced Materials},
pages = {2669-2674},
peerreviewed = {Yes},
title = {{Finding} {Auxetic} {Frameworks} in {Periodic} {Tessellations}},
volume = {23},
year = {2011}
}
@article{faucris.117918064,
author = {Langnese, John E. and Leugering, Günter},
doi = {10.1016/0022-0396(91)90145-Y},
faupublication = {no},
journal = {Journal of Differential Equations},
pages = {355-388},
peerreviewed = {Yes},
title = {{UNIFORM} {STABILIZATION} {OF} {A} {NONLINEAR} {BEAM} {BY} {NONLINEAR} {BOUNDARY} {FEEDBACK}},
url = {http://www.sciencedirect.com/science/article/pii/002203969190145Y},
volume = {91},
year = {1991}
}
@article{faucris.109450484,
author = {Jahn, Johannes},
doi = {10.1007/s10589-014-9674-8},
faupublication = {yes},
journal = {Computational Optimization and Applications},
note = {UnivIS-Import:2015-03-09:Pub.2014.nat.dma.pama21.aderiv},
pages = {393 - 411},
peerreviewed = {Yes},
title = {{A} derivative-free descent method in set optimization},
volume = {60},
year = {2015}
}
@inproceedings{faucris.117912344,
abstract = {The authors describe a general model for vibrating networks and show how the model applies to networks of elastic strings or Timoshenko beams. They indicate how hyperbolic energy estimates for first-order systems yield the a priori estimates needed to prove exact controllability and stabilizability. They show how the model can be generalized to allow mixed networks of strings and beams. They also discuss generalizations of the Timoshenko beam and their relation on the present model.},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
booktitle = {Decision and Control},
date = {1992-12-16/1992-12-18},
doi = {10.1109/CDC.1992.371260},
faupublication = {no},
isbn = {0-7803-0872-7},
keywords = {Yield estimation, Controllability},
month = {Jan},
pages = {3003-3008},
peerreviewed = {unknown},
publisher = {IEEE Xplore},
title = {{ON} {HYPERBOLIC} {SYSTEMS} {ASSOCIATED} {WITH} {THE} {MODELING} {AND} {CONTROL} {OF} {VIBRATING} {NETWORKS}},
url = {http://ieeexplore.ieee.org/document/371260/},
year = {1992}
}
@article{faucris.113899544,
abstract = {We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small. © 2014 Elsevier B.V. All rights reserved.},
author = {Gugat, Martin},
doi = {10.1016/j.sysconle.2014.01.007},
faupublication = {yes},
journal = {Systems & Control Letters},
keywords = {Anti-damping; Boundary feedback; Damping; Decay rate; Exponential stability; Hyperbolic partial differential equation; Nonlinear wave equation; Semilinear wave equation; Telegraph equation},
note = {UnivIS-Import:2015-03-09:Pub.2014.nat.dma.lama1.bounda},
pages = {72-84},
peerreviewed = {Yes},
title = {{Boundary} feedback stabilization of the telegraph equation: {Decay} rates for vanishing damping term},
url = {http://ac.els-cdn.com/S0167691114000279/1-s2.0-S0167691114000279-main.pdf?_tid=631b42fa-9efc-11e3-83ef-00000aab0f26&acdnat=1393429438_c7a54e1446ab014020ff9d6d7536964a},
volume = {66},
year = {2014}
}
@article{faucris.106690364,
author = {Hante, Falk and Sigalotti, Mario and Tucsnak, Marius},
doi = {10.1016/j.jde.2012.01.037},
faupublication = {no},
journal = {Journal of Differential Equations},
pages = {5569--5593},
peerreviewed = {Yes},
title = {{On} conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping},
volume = {252},
year = {2012}
}
@article{faucris.117905084,
abstract = {Distributed load control of motions governed by an abstract partial integrodifferential equation is studied. First a new system-theoretic approach to a mild solution theory of equations arising in viscoelasticity of fading memory type is developed. Then it is shown that control results for the damped abstract wave equation devolve to a special class of “virgin” material with fading memory.},
author = {Leugering, Günter},
doi = {10.1080/00036818408839521},
faupublication = {no},
journal = {Applicable Analysis},
keywords = {93B05; 45K05; 73K05},
month = {Jan},
pages = {221-243},
peerreviewed = {Yes},
title = {{EXACT} {CONTROLLABILITY} {IN} {VISCOELASTICITY} {OF} {FADING} {MEMORY} {TYPE}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00036818408839521},
volume = {18},
year = {1984}
}
@article{faucris.123598024,
abstract = {We present a novel approach for gradient based maximization of phononic band gaps. The approach is a geometry projection method combining parametric shape optimization with density based topology optimization. By this approach, we obtain, in a two dimension setting, cellular structures exhibiting relative and normalized band gaps of more than 8 and 1.6, respectively. The controlling parameter is the minimal strut size, which also corresponds with the obtained stiffness of the structure. The resulting design principle is manually interpreted into a three dimensional structure from which cellular metal samples are fabricated by selective electron beam melting. Frequency response diagrams experimentally verify the numerically determined phononic band gaps of the structures. The resulting structures have band gaps down to the audible frequency range, qualifying the structures for an application in noise isolation.},
author = {Wormser, Maximilian and Wein, Fabian and Stingl, Michael and Körner, Carolin},
doi = {10.3390/ma10101125},
faupublication = {yes},
journal = {Materials},
keywords = {phononic band gap; additive manufacturing; selective electron beam melting; cellular materials; metamaterials; topology optimization; parametric shape optimization; gradient based optimization},
peerreviewed = {Yes},
title = {{Design} and {Additive} {Manufacturing} of {3D} {Phononic} {Band} {Gap} {Structures} {Based} on {Gradient} {Based} {Optimization}},
volume = {10},
year = {2017}
}
@article{faucris.107387104,
abstract = {The goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure. A natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable. As an alternative, we propose a new approach, which is based on a nonlinear semidefinite low-rank approximation of the semidefinite dual. We introduce an algorithm based on this approach and analyze its convergence properties. The article is concluded by numerical experiments proving the effectiveness of the new approach},
author = {Stingl, Michael and Kocvara, Michal and Leugering, Günter},
doi = {10.1137/080717122},
faupublication = {yes},
journal = {SIAM Journal on Optimization},
pages = {524--547},
peerreviewed = {Yes},
title = {{Free} {Material} {Optimization} with {Fundamental} {Eigenfrequency} {Constraints}},
volume = {20},
year = {2009}
}
@book{faucris.115716084,
abstract = {Water supply- and drainage systems and mixed water channel systems are networks whose high dynamic is determined and/or affected by consumer habits on drinking water on the one hand and by climate conditions, in particular rainfall, on the other hand. According to their size, water networks consist of hundreds or thousands of system elements. Moreover, different types of decisions (continuous and discrete) have to be taken in the water management. The networks have to be optimized in terms of topology and operation by targeting a variety of criteria. Criteria may for example be economic, social or ecological ones and may compete with each other. The development of complex model systems and their use for deriving optimal decisions in water management is taking place at a rapid pace. Simulation and optimization methods originating in Operations Research have been used for several decades; usually with very limited direct cooperation with applied mathematics. The research presented here aims at bridging this gap, thereby opening up space for synergies and innovation. It is directly applicable for relevant practical problems and has been carried out in cooperation with utility and dumping companies, infrastructure providers and planning offices. A close and direct connection to the practice of water management has been established by involving application-oriented know-how from the field of civil engineering. On the mathematical side all necessary disciplines were involved, including mixed-integer optimization, multi-objective and facility location optimization, numerics for cross-linked dynamic transportation systems and optimization as well as control of hybrid systems. Most of the presented research has been supported by the joint project "Discret continuous optimization of dynamic water systems" of the federal ministry of education and research (BMBF).},
author = {Martin, Alexander and Klamroth, Kathrin and Lang, Jens and Leugering, Günter and Morsi, Antonio and Oberlack, Martin and Ostrowski, Manfred and Rosen, Roland},
faupublication = {yes},
peerreviewed = {Yes},
publisher = {Birkhäuser},
series = {International Series of Numerical Mathematics},
title = {{Mathematical} {Optimization} of {Water} {Networks}},
volume = {162},
year = {2012}
}
@inproceedings{faucris.111074964,
abstract = {We consider a network of Euler-Bernoulli- and Rayleigh-beams. For the sake of simplicity, we concentrate on scalar displacements coupled to torsion. We show that the model is well-posed in appropriate ramification spaces. We then describe a dynamic nonoverlapping domain decomposition procedure of the network into its individual edges and provide a proof of convergence. Further, we formulate typical optimal control problems, related to exact controllability. The optimality system is solved using conjugate gradients. Various numerical examples illustrate the method.},
author = {Leugering, Günter and Rathmann, Wigand},
faupublication = {yes},
keywords = {Euler-Bernoulli- and Rayleigh beams;network models;nonoverlapping domain decompositions;optimal controls},
month = {Jan},
pages = {199-232},
peerreviewed = {unknown},
title = {{On} modeling, analysis and simulation of optimal control problems for dynamic networks of {Euler}-{Bernoulli}- and {Rayleigh}-beams},
volume = {218},
year = {2001}
}
@article{faucris.124195544,
abstract = {In this article we study an optimal control problem for a nonlinear monotone Dirichlet problem where the controls are taken as matrix-valued coefficients in L-infinity (Omega; R-NxN). For the exemplary case of a tracking cost functional, we derive first order optimality conditions. This first part is concerned with the general case of matrix-valued coefficients under some hypothesis, while the second part focuses on the special class of diagonal matrices.},
author = {Kogut, Peter I. and Kupenko, Ol'Ga P. and Leugering, Günter},
doi = {10.4171/ZAA/1530},
faupublication = {yes},
journal = {Zeitschrift für Analysis und ihre Anwendungen},
keywords = {Nonlinear monotone Dirichlet problem;control in coefficients;adjoint equation},
month = {Jan},
pages = {85-108},
peerreviewed = {Yes},
title = {{Optimal} {Control} in {Matrix}-{Valued} {Coefficients} for {Nonlinear} {Monotone} {Problems}: {Optimality} {Conditions} {I}},
volume = {34},
year = {2015}
}
@article{faucris.109406264,
abstract = {The one-dimensional isothermal Euler equations are a well-known model for the flow of gas through a pipe. An essential part of the model is the source term that models the influence of gravity and friction on the flow. In general the solutions of hyperbolic balance laws can blow-up in finite time. We show the existence of initial data with arbitrarily large C^{1}-norm of the logarithmic derivative where no blow up in finite time occurs. The proof is based upon the explicit construction of product solutions. Often it is desirable to have such analytical solutions for a system described by partial differential equations, for example to validate numerical algorithms, to improve the understanding of the system and to study the effect of simplifications of the model. We present solutions of different types: In the first type of solutions, both the flow rate and the density are increasing functions of time. We also present a second type of solutions where on a certain time interval, both the flow rate and the pressure decrease. In pipeline networks, the bi-directional use of the pipelines is sometimes desirable. In this paper we present a classical solution of the isothermal Euler equations where the direction of the gas flow changes. In the solution, at the time before the direction of the flow is reversed, the gas flow rate is zero everywhere in the pipe.},
author = {Gugat, Martin and Ulbrich, Stefan},
doi = {10.1016/j.jmaa.2017.04.064},
faupublication = {yes},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Global classical solutions; Ideal gas; Bi-directional flow; Transsonic flow},
pages = {439–452},
peerreviewed = {Yes},
title = {{The} isothermal {Euler} equations for ideal gas with source term: {Product} solutions, flow reversal and no blow up},
url = {http://www.sciencedirect.com/science/article/pii/S0022247X17304274},
volume = {454},
year = {2017}
}
@article{faucris.124194884,
abstract = {Commonly applied models to study vocal fold vibrations in combination with air flow distributions are self-sustained physical models of the larynx consisting of artificial silicone vocal folds. Choosing appropriate mechanical parameters and layer geometries for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In earlier work by Schmidt et al. [J. Acoust. Soc. Am. 129, 2168-2180 (2011)], the authors presented an approach in which material parameters of a static numerical vocal fold model were optimized to achieve an agreement of the displacement field with data retrieved from hemilarynx experiments. This method is now generalized to a fully transient setting. Moreover in addition to the material parameters, the extended approach is capable of finding optimized layer geometries. Depending on chosen material restriction, significant modifications of the reference geometry are predicted. The additional flexibility in the design space leads to a significantly more realistic deformation behavior. At the same time, the predicted biomechanical and geometrical results are still feasible for manufacturing physical vocal fold models consisting of several silicone layers. As a consequence, the proposed combined experimental and numerical method is suited to guide the construction of physical vocal fold models. (C) 2013 Acoustical Society of America.},
author = {Schmidt, Bastian and Leugering, Günter and Stingl, Michael and Hüttner, Björn and Agaimy, Abbas and Döllinger, Michael},
doi = {10.1121/1.4812253},
faupublication = {yes},
journal = {Journal of the Acoustical Society of America},
pages = {1261-1270},
peerreviewed = {Yes},
title = {{Material} and shape optimization for multi-layered vocal fold models using transient loadings},
volume = {134},
year = {2013}
}
@article{faucris.115625004,
abstract = {Using the concept of contingent epiderivative, we generalize the notion of subdifferential to a cone-convex set-valued map. Properties of the subdifferential are presented and an optimality condition is discussed.},
author = {Jahn, Johannes and Baier, J.},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Convex analysis; Set-valued analysis; Subdifferentials; Vector optimization},
note = {UnivIS-Import:2015-03-05:Pub.1999.nat.dma.pama21.onsubd},
pages = {233-240},
peerreviewed = {Yes},
title = {{On} {Subdifferentials} of {Set}-{Valued} {Maps}},
volume = {100},
year = {1999}
}
@article{faucris.116677044,
abstract = {We consider a location problem where the distribution of the existing facilities is described by a probability distribution and the transportation cost is given by a combination of transportation cost in a network and continuous distance. The motivation is that in many cases transportation cost is partly given by the cost of travel in a transportation network whereas the access to the network and the travel from the exit of the network to the new facility is given by a continuous distance. © 2007 Springer-Verlag.},
author = {Gugat, Martin and Pfeiffer, Barbara},
doi = {10.1007/s00186-007-0165-x},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
keywords = {Facility planning; Mixed distance; Regional demand; Stochastic optimization; Weber problem},
note = {UnivIS-Import:2015-03-09:Pub.2007.nat.dma.zentr.weberp},
pages = {419-449},
peerreviewed = {Yes},
title = {{Weber} problems with mixed distances and regional demand},
url = {http://www.springerlink.com/content/k649343352n310q5/fulltext.pdf},
volume = {66},
year = {2007}
}
@inproceedings{faucris.117639104,
abstract = {In this article, we present the Free Material Optimization (FMO) problem for plates and shells based on Naghdi's shell model. In FMO - a branch of structural optimization - we search for the ultimately best material properties in a given design domain loaded by a set of given forces. The optimization variable is the full material tensor at each point of the design domain. We give a basic formulation of the problem and prove existence of an optimal solution. Lagrange duality theory allows to identify the basic problem as the dual of an infinite-dimensional convex nonlinear semidefinite program. After discretization by the finite element method the latter problem can be solved using a nonlinear SDP code. The article is concluded by a few numerical studies.},
author = {Gaile, Stefanie and Leugering, Günter and Stingl, Michael},
booktitle = {Proceedings of the 23rd IFIP TC 7 Conference on System Modelling and Optimization},
date = {2007-07-23/2007-07-27},
faupublication = {yes},
month = {Jan},
pages = {239-250},
peerreviewed = {unknown},
publisher = {Springer Verlag},
title = {{Free} material optimization for plates and shells},
venue = {Cracow},
volume = {312},
year = {2009}
}
@article{faucris.116675724,
abstract = {We consider a finite string where, at both end points, a homogeneous Dirichlet boundary condition holds. One boundary point is fixed, and the other is moving; hence the length of the string is changing in time. The string is controlled through the movement of this boundary point. We consider movements of the boundary that are Lipschitz continuous. Only movements for which at the given finite terminal time the string has the same length as at the beginning are admissible. Moreover, we impose an upper bound for the Lipschitz constant of the movement that is smaller than the speed of wave propagation. We consider the optimal control problem to find an admissible movement for which at the given terminal time the energy of the string is minimal. We give a sufficient condition for the existence and uniqueness of an optimal movement and construct an optimal control movement. © 2007 Society for Industrial and Applied Mathematics.},
author = {Gugat, Martin},
doi = {10.1137/06065636x},
faupublication = {yes},
journal = {SIAM Journal on Control and Optimization},
keywords = {Control constraint; Moving boundary; Optimal boundary control; Optimal control of PDEs; Optimal energy control; Optimal shape; PDE-constrained optimization; Wave equation; 49K20; 35L05},
note = {UnivIS-Import:2015-03-09:Pub.2007.nat.dma.zentr.optima_0},
pages = {1705-17025},
peerreviewed = {Yes},
title = {{Optimal} {Energy} {Control} in {Finite} {Time} by varying the {Length} of the {String}},
url = {http://www2.am.uni-erlangen.de/~gugat/sicon2007.pdf},
volume = {46},
year = {2007}
}
@article{faucris.107378744,
author = {Bischoff, Martin and Jahn, Johannes and Köbis, Elisabeth},
faupublication = {yes},
journal = {Optimization},
pages = {361-380},
peerreviewed = {Yes},
title = {{Hard} uncertainties in multiobjective layout optimization of photovoltaic power plants},
volume = {66},
year = {2017}
}
@article{faucris.117450344,
abstract = {We consider an exact boundary control problem for the wave equation with given initial and terminal data and Dirichlet boundary control. The aim is to steer the state of the system that is defined on a given domain to a position of rest in finite time. The optimal control that is obtained as the solution of the problem depends on the data that define the problem, in particular on the domain. Often for the numerical solution of the control problem, this given domain is replaced by a polygon. This is the motivation to study the convergence of the optimal controls for the polygon to the optimal controls for the given domain. To study the convergence, the values of the optimal controls that are defined on the boundaries of the approximating polygons are mapped in the normal directions of the polygon to control functions defined on the boundary of the original domain. This map has already been used by Bramble and King, Deckelnick, Guenther and Hinze and by Casas and Sokolowski. Using this map, we can show the strong convergence of the transformed controls as the polygons approach the given domain. An essential tool to obtain the convergence is a regularization term in the objective functions to increase the regularity of the state.},
author = {Gugat, Martin and Sokolowski, Jan},
doi = {10.1080/00036811.2012.724404},
faupublication = {yes},
journal = {Applicable Analysis},
keywords = {wave equation; Dirichlet boundary control; exact control; optimal control; domain sensitivity; polygonal domain; 49J20; 35L05; 35L53},
note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.lama1.anoteo},
pages = {2200-2214},
peerreviewed = {Yes},
title = {{A} note on the approximation of {Dirichlet} boundary control problems for the wave equation on curved domains},
url = {http://www.tandfonline.com/doi/abs/10.1080/00036811.2012.724404},
volume = {92},
year = {2012}
}
@incollection{faucris.117650104,
abstract = {We consider shape optimization for objects illuminated by light. More precisely, we focus on time-harmonic solutions of the Maxwell system in **curl-curl**-form scattered by an arbitrary shaped rigid object. Given a class of cost functionals, including the scattered energy and the extinction cross section, we develop an adjoint-based shape optimization scheme which is then applied to two key applications.},
author = {Semmler, Johannes and Pflug, Lukas and Stingl, Michael and Leugering, Günter},
booktitle = {New Trends in Shape Optimization},
doi = {10.1007/978-3-319-17563-8_11},
editor = {Aldo Pratelli, Günter Leugering},
faupublication = {yes},
keywords = {Partial Differential Equations; Systems Theory; Control},
pages = {251-269},
peerreviewed = {unknown},
publisher = {Springer},
series = {International Series of Numerical Mathematics},
title = {{Shape} {Optimization} in {Electromagnetic} {Applications}},
volume = {166},
year = {2015}
}
@article{faucris.120837024,
author = {Rathmann, Wigand and Krug, Andreas},
faupublication = {no},
journal = {Infoplaner},
pages = {44--45},
peerreviewed = {No},
title = {{Grundlagen} {FEM}: {Galerkin}-{Verfahren}},
year = {2005}
}
@article{faucris.115449004,
abstract = {In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.},
author = {Jahn, Johannes and Rauh, R.},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
keywords = {Convex and set-valued analysis; Optimality conditions; Vector optimization},
note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.pama21.contin},
pages = {193-211},
peerreviewed = {Yes},
title = {{Contingent} {Epiderivatives} and {Set}-{Valued} {Optimization}},
volume = {46},
year = {1997}
}
@article{faucris.107408444,
abstract = {In this paper, we study a Dirichlet optimal control problem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The coefficients may degenerate and, therefore, the problems may exhibit the so-called Lavrentieff phenomenon and non-uniqueness of weak solutions. We consider the solvability of this problem in the class of W-variational solutions. Using a concept of variational convergence of constrained minimization problems in variable spaces, we prove the existence of W-solutions to the optimal control problem and provide the way for their approximation. We emphasize that control problems of this type are important in material and topology optimization as well as in damage or life-cycle optimization.},
author = {Kogut, Peter I. and Leugering, Günter},
doi = {10.1007/s10957-011-9840-4},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Degenerate elliptic equations;Control in coefficients;Weighted Sobolev spaces;Lavrentieff phenomeno;Variational convergence},
pages = {205--232},
peerreviewed = {Yes},
title = {{Optimal} {L1}-{Control} in {Coefficients} for {Dirichlet} {Elliptic} {Problems}: {W}-{Optimal} {Solutions}},
volume = {150},
year = {2011}
}
@article{faucris.106725564,
abstract = {

Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot be proved or is even violated. In particular, in these cases standard nonsmooth methods cannot be used. In this paper, we propose a new approach to develop a converging descent method for this class of nonsmooth functions. This approach is based on continuous outer subdifferentials introduced by us. Further, we introduce on this basis a conceptual optimization algorithm and prove its global convergence. This leads to a constructive approach enabling us to create a converging descentmethod. Within the algorithmic framework, neither semismoothness nor calculation of exact subgradients are required. This is in contrast to other approaches which are usually based on the assumption of semismoothness of the

objective function.

},
author = {Knossalla, Martin},
doi = {10.1080/02331934.2018.1426579},
faupublication = {yes},
journal = {Optimization},
keywords = {Mathematical programming; nonsmooth optimization; parametric optimization; variational analysis and optimization},
month = {Jan},
pages = {1-21},
peerreviewed = {Yes},
title = {{Minimization} of marginal functions in mathematical programming based on continuous outer subdifferentials},
year = {2018}
}
@incollection{faucris.122351724,
abstract = {A hydrodynamic process model based on shallow water equations is discretized on 1D-networks with the method of finite volumes. Based on the finite volumes we replace algebraic coupling conditions by a consistent finite volume junction model. We use discrete adjoint computation for one step Runge-Kutta schemes to generate fast and robust gradients for descent methods. We use the descent methods to generate an optimal control for an example network and discuss the computational results.},
author = {Hild, Johannes and Leugering, Günter},
booktitle = {Mathematical Optimization of Water Networks},
doi = {10.1007/978-3-0348-0436-3_8},
editor = {Birkhäuser Basel},
faupublication = {yes},
isbn = {978-3-0348-0435-6},
pages = {pp 129-150},
peerreviewed = {unknown},
publisher = {Springer Basel},
series = {International Series of Numerical Mathematics},
title = {{Real}-{Time} {Control} of {Urban} {Drainage} {Systems}},
volume = {162},
year = {2012}
}
@article{faucris.117916084,
abstract = {We present an algorithm that automatically registers one segmented contour in a frame of the video sequence to the contour in the next frame to derive discrete 2-D trajectories of PE vibrations. By concatenation of the obtained transformations this approach provides a total registration of PE segment contours. We suggest a mixed-integer programming formulation for the problem that combines an advanced outlier and deformation handling with the introduction of dummy points in regions that newly open up, and that includes normal information in the objective function to avoid unwanted deformations. Numerical experiments show that the implemented alternate convex search algorithm produces robust results which is demonstrated at the example of five high-speed recordings of laryngectomee subjects. (C) 2007 Elsevier B.V. All rights reserved.},
author = {Stiglmayr, Michael and Schwarz, Raphael and Klamroth, Kathrin and Leugering, Günter and Lohscheller, Jörg},
doi = {10.1016/j.media.2007.12.001},
faupublication = {yes},
journal = {Medical Image Analysis},
keywords = {substitute voice;PE segment;digital high-speed videos;point matching;shape registration;generalized assignment problem;2-D trajectories},
pages = {318-334},
peerreviewed = {Yes},
title = {{Registration} of {PE} segment contour deformations in digital high-speed videos},
url = {http://www.sciencedirect.com/science/article/pii/S1361841507001120},
volume = {12},
year = {2008}
}
@article{faucris.117419984,
abstract = {Our goal is to design brittle composite materials yielding maximal energy dissipation for a given static load case. We focus on the effect of variation of fiber shapes on resulting crack paths and thus on the fracture energy. To this end, we formulate a shape optimization problem, in which the cost function is the fracture energy and the state problem consists in the determination of the potentially discontinuous displacement field in the two-dimensional domain. Thereby, the behavior at the crack surfaces is modeled by cohesive laws. We impose a nonpenetration condition to avoid interpenetration of opposite crack sides. Accordingly, the state problem is formulated as variational inequality. This leads to potential nondifferentiability of the shape-state mapping. For the numerical solution, we derive first-order information in the form of subgradients. We conclude the article by numerical results.},
author = {Prechtel, Marina and Leugering, Günter and Steinmann, Paul and Stingl, Michael},
doi = {10.1007/s10957-012-0094-6},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Our goal is to design brittle composite materials yielding maximal energy dissipation for a given static load case. We focus on the effect of variation of fiber shapes on resulting crack paths and thus on the fracture energy. To this end, we formulate a shape optimization problem, in which the cost function is the fracture energy and the state problem consists in the determination of the potentially discontinuous displacement field in the two-dimensional domain. Thereby, the behavior at the crack surfaces is modeled by cohesive laws. We impose a nonpenetration condition to avoid interpenetration of opposite crack sides. Accordingly, the state problem is formulated as variational inequality. This leads to potential nondifferentiability of the shape-state mapping. For the numerical solution, we derive first-order information in the form of subgradients. We conclude the article by numerical results.},
note = {UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.optima},
pages = {962-985},
peerreviewed = {Yes},
title = {{Optimal} {Design} of {Brittle} {Composite} {Materials}: a {Nonsmooth} {Approach}},
volume = {155},
year = {2012}
}
@article{faucris.124195324,
abstract = {In this article the authors continue the discussion in [9] about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measurements. In the present paper we prove the identifiability of varying densities of a planar tree-like network of strings along with the complete information on the graph, i.e. the lengths of the edges, the edge degrees and the angles between neighbouring edges. The results are achieved using the Titchmarch-Weyl function for the spectral problem and the Steklov-Poincare operator for the dynamic wave equation on the tree. The general result is obtained by a peeling argument which reduces the inverse problem layer-by-layer from the leaves to the clamped root of the tree. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim},
author = {Avdonin, Sergei and Abdon, Choque Rivero and Leugering, Günter and Mikhaylov, Victor},
doi = {10.1002/zamm.201400126},
faupublication = {yes},
journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik},
keywords = {Inverse problem;planar tree of strings;Titchmarch-Weyl-matrix;dynamic Steklov-Poincare operator;leaf-peeling method},
pages = {1490-1500},
peerreviewed = {Yes},
title = {{On} the inverse problem of the two-velocity tree-like graph},
volume = {95},
year = {2015}
}
@article{faucris.122286384,
author = {Leugering, Günter and Pflug, Lukas and Spinola, Michele},
doi = {10.1002/cite.201650478},
faupublication = {yes},
journal = {Chemie-Ingenieur-Technik},
pages = {1366-1367},
peerreviewed = {unknown},
title = {{Adjungierten}-basierte {Prozessoptimierung} der {Nanopartikel}-{Synthese}},
volume = {88},
year = {2016}
}
@article{faucris.111078044,
abstract = {We consider the problem of boundary optimal control of a wave equation with boundary dissipation by the way of time-domain decomposition of the corresponding optimality system. We develop an iterative algorithm which shows that the decomposed optimality system corresponds to local-in-time optimal control problems which can be treated in parallel. We show convergence of the algorithm. Finally, we provide a time discretization which is reminiscent of an instantaneous control scheme. We thereby also contribute to the problem of convergence of such schemes. (C) 2002 Elsevier Science B.V. All rights reserved.},
author = {Langnese, John E. and Leugering, Günter},
doi = {10.1016/S0167-6911(02)00268-2},
faupublication = {no},
journal = {Systems & Control Letters},
keywords = {time-domain decomposition;optimality systems;instantaneous control},
pages = {229-242},
peerreviewed = {Yes},
title = {{Time}-domain decomposition of optimal control problems for the wave equation},
url = {http://www.sciencedirect.com/science/article/pii/S0167691102002682},
volume = {48},
year = {2003}
}
@article{faucris.111754104,
author = {Hante, Falk},
doi = {10.1002/pamm.201610380},
faupublication = {yes},
journal = {Proceedings in Applied Mathematics and Mechanics},
pages = {783--784},
peerreviewed = {Yes},
title = {{On} the relaxation gap for {PDE} mixed-integer optimal control problems},
volume = {16},
year = {2016}
}
@inproceedings{faucris.122718904,
abstract = {For master students of the process technology and energy technology we offer a course on simulation of transport processes. Two aims are focused:

The students should learn or repeat the basics in using a simulation tools.

They should learn to combine specialized knowledge with mathematical concepts to simulate a technical process.

In the first part of the course the students collect first experiences in programming by modeling a Rankine cycle using Matlab. Hereby they discuss the quality of the presented mathematical model and possible improvements. The students are accompanied by the lecturers of the lecture "Transport processes" (master studies) and “Mathematics for Engineers” (bachelor studies). While working on the computer learners can discuss their questions, programming ideas and difficulties with each other and the trainers and they receive immediate feedbacks. The second part of the course is focuses on simple heat transfer processes described by ODE or PDE models. Therefore some mathematical concepts (e.g. linear equation systems) are needed, but they have learned it about three years ago.

Up to now the mathematical models of the technical processes and the repetition of the mathematical basics were presented as talks during the lectures with little time remained for the discussion. But the students need enough time to reconsider the introduced topics. We have seen, that this process needs more time then scheduled, e.g. to understand the way to describe the first derivative of a function on a interval by a system of linear equation system.

Now we are working on a didactic reorganization (flipped classroom) of our course, so that the students will have enough time, to repeat subjects needed in our course.

Therefore on-line learning modules and formative on-line tests have to be finished to prepare the single sessions. Thus questions can be discussed quite early and it remains more time to discuss, e.g. improvements of the models. By using the flipped classroom concept the students will be motivated to work more independently and they may reach a better understanding by using the digital learning materials as starting point for the considerations. Thus we will generate a more active participation in the teaching and learning events and better learner’s results can be achieved.

In my talk I would like to discuss these ideas and I will give a short status report of the actual course.

}, author = {Rathmann, Wigand and Wensing, Michael and Zepf, Stefanie}, booktitle = {The 18th SEFI Mathematics working Group Seminar}, date = {2016-06-27/2016-06-29}, faupublication = {yes}, peerreviewed = {unknown}, title = {{Flipped} classroom in interdisciplinary course}, url = {http://www.math.chalmers.se/SEFIMWG2016/Book%20of%20accepted%20abstracts/part49.htm}, venue = {Gothenburg}, year = {2016} } @book{faucris.109061964, address = {Berlin}, editor = {Jahn, Johannes and Krabs, W.}, faupublication = {yes}, note = {UnivIS-Import:2015-05-08:Pub.1987.nat.dma.pama21.dualit}, publisher = {Springer}, title = {{Recent} {Advances} and {Historical} {Development} of {Vector} {Optimization}}, year = {1987} } @article{faucris.113909884, abstract = {We consider the problem to control a vibrating string to rest in a given finite time. The string is fixed at one end and controlled by Neumann boundary control at the other end. We give an explicit representation of the
There are very few results about analytic solutions of problems of optimal control with minimal *L* ^{∞} norm. In this paper, we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. We start in the zero position and consider a problem of exact control, that is, we want to reach a given terminal state in a given finite time. Our aim is to find a control with minimal *L* ^{∞} norm that steers the system to the target.

We give the analytic solution for certain classes of target points, for example, target points that are given by constant functions. For such targets with zero velocity, the analytic solution has been given by Bennighof and Boucher in Ref. 1.

}, author = {Gugat, Martin}, doi = {10.1023/A:1016091803139}, faupublication = {no}, journal = {Journal of Optimization Theory and Applications}, keywords = {Optimal Control; Wave Equation; Analytic Solution; Distributed Parameter Systems}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.analyt}, pages = {397-421}, peerreviewed = {Yes}, title = {{Analytic} {Solutions} of {L}-infinity optimal control problems for the wave equation}, volume = {114}, year = {2002} } @article{faucris.207256326, abstract = {The haze factor, which describes the fraction of light that is scattered when passing through a transparent material, is of general importance for any optical device, from milk glass shielding visibility while providing ambient lighting to solar cells that are optimized by sophisticated light management layers. Often, such active layers are fabricated from particulate materials that are deposited as thin films on a substrate. Here, the effect of structural arrangement, position, and orientation of particles on the resulting haze factor is investigated. A mathematical optimization model that iteratively alters the particle layer structure to maximize or minimize the haze factor for a range of optimization scenarios is designed. Colloidal self-assembly techniques are then used to replicate typical particle structures found in the optimized designs and correlate the macroscopically measured haze values to the predictions of the optimization. The results indicate general design rules that control the haze value in particle layers. Non close-packed structures with distributed scatterers and high degrees of order provide minimal haze values while chain-like arrangements and small clusters maximize the haze of a particle layer. Finally, the findings are transferred to metal nanohole films as model transparent electrodes with controlled haze values.}, author = {Semmler, Johannes and Bley, Karina and Klupp Taylor, Robin and Stingl, Michael and Vogel, Nicolas}, doi = {10.1002/adfm.201806025}, faupublication = {yes}, journal = {Advanced Functional Materials}, peerreviewed = {unknown}, title = {{Particulate} {Coatings} with {Optimized} {Haze} {Properties}}, url = {https://onlinelibrary.wiley.com/doi/full/10.1002/adfm.201806025}, volume = {5}, year = {2018} } @article{faucris.109705684, abstract = {This paper concerns the generalization and regularization of a nonlinear scalarization method by Pascoletti and Serafini, [14], to abstract partially ordered Banach spaces. In particular, we put emphasis on the possibility that the ordering cone might have an empty interior. All this is motivated by applying the method to a vector optimization problem with PDE-constraints. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA.}, author = {Leugering, Günter and Schiel, Ralph}, doi = {10.1002/gamm.201210014}, faupublication = {yes}, journal = {GAMM-Mitteilungen}, keywords = {Gerstewitz function; Nonlinear scalarization; Nonsolid ordering cones; Optimal control; Vector optimization}, pages = {209-225}, peerreviewed = {Yes}, title = {{Regularized} nonlinear scalarization for vector optimization problems with {PDE}-constraints}, volume = {35}, year = {2012} } @article{faucris.112245584, abstract = {We consider a star-shaped network consisting of a single node with N ≥ 3 connected arcs. The dynamics on each arc is governed by the wave equation. The arcs are coupled at the node and each arc is controlled at the other end. Without assumptions on the lengths of the arcs, we show that if the feedback control is active at all exterior ends, the system velocity vanishes in finite time. In order to achieve exponential decay to zero of the system velocity, it is not necessary that the system is controlled at all N exterior ends, but stabilization is still possible if, from time to time, one of the feedback controllers breaks down. We give sufficient conditions that guarantee that such a switching feedback stabilization where not all controls are necessarily active at each time is successful. © American Institute of Mathematical Sciences.}, author = {Gugat, Martin and Sigalotti, Mario}, doi = {10.3934/nhm.2010.5.299}, faupublication = {yes}, journal = {Networks and Heterogeneous Media}, keywords = {Feedback stabilization of pdes; Hyperbolic pde; Network; Robustness; Switching control; Switching feedback; Wave equation}, note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.starso}, pages = {299-314}, peerreviewed = {Yes}, title = {{Stars} of vibrating strings: {Switching} boundary feedback stabilization}, url = {http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5215}, volume = {5}, year = {2010} } @article{faucris.117917404, abstract = {It is shown that the vibrations of a viscoelastic beam can be steered to rest in minimal time using a L

We consider refinement of finite element discretizations by splitting nodes along edges. For

this process, we derive asymptotic expansions of Galerkin solutions of linear second-order

elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for

functionals such as the total potential energy, minimization of which decreases the approxi-

mation error in the energy norm. Hence, these sensitivities can be used to define indicators for

local h-refinement. Our results suggest that this procedure leads to an efficient adaptive re-

finement method. This presentation is concerned with a model problem in 1d. The extension

of this concept to higher dimensions will be the subject of forthcoming publications.

},
author = {Friederich, Jan and Leugering, Günter and Steinmann, Paul},
doi = {10.1002/gamm.201210012},
faupublication = {yes},
journal = {GAMM-Mitteilungen},
note = {UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.anadap},
pages = {175-190},
peerreviewed = {unknown},
title = {{An} adaptive finite element method based on sensitivities for node insertion},
url = {http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/full},
volume = {35},
year = {2012}
}
@article{faucris.119409444,
abstract = {The problem of maximizing the performance in a fiber distributed data interface (FDDI) computer network is formulated as a cooperative n-player game. Solutions of this game can be obtained by solving special optimization problems. Using the models and formulas developed by Tangemann (Ref. 1) and Klehmet (Ref. 2) for the mean waiting times, the resulting optimization problems are presented and numerical results are given.},
author = {Jahn, Johannes and Häßler, S.},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Cooperative games; Timed token rotation protocols; Vector optimization},
note = {UnivIS-Import:2015-03-09:Pub.2000.nat.dma.pama21.gameth},
pages = {463-474},
peerreviewed = {Yes},
title = {{Game}-{Theoretic} {Approach} to the {Optimization} of {FDDI} {Computer} {Networks}},
volume = {106},
year = {2000}
}
@incollection{faucris.119669484,
address = {Heidelberg},
author = {Eichfelder, Gabriele and Jahn, Johannes},
booktitle = {Recent Developments in Vector Optimization},
doi = {10.1007/978-3-642-21114-0},
editor = {Q.H. Ansari, J.-C. Yao},
faupublication = {yes},
isbn = {978-3-642-21113-3},
note = {UnivIS-Import:2015-04-20:Pub.2012.nat.dma.pama21.vector},
pages = {1-27},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Vector} {Optimization} {Problems} and {Their} {Solution} {Concepts}},
url = {http://www.springer.com/business+%26+management/operations+research/book/978-3-642-21113-3},
year = {2012}
}
@article{faucris.115613344,
abstract = {In this paper we consider the behaviour of the multipliers for one-parametric semi-infinite programs near critical parameters, where the Mangasarian-Fromovitz constraint qualification can be violated. The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers. © Springer-Verlag 1999.},
author = {Gugat, Martin},
doi = {10.1007/s10107990058a},
faupublication = {no},
journal = {Mathematical Programming},
keywords = {Gauvin's theorem; Karush-Kuhn-Tucker multiplier; Mangasarian-Fromovitz constraint qualification; Modulus of multiplier growth; Parametric nonconvex program; Semi-infinite program; Singular parameters; Uniform Mangasarian-Fromovitz condition},
note = {UnivIS-Import:2015-03-05:Pub.1999.nat.dma.lama1.aparam},
pages = {643-653},
peerreviewed = {Yes},
title = {{A} parametric view on the {Mangasarian}-{Fromovitz} constraint qualification},
volume = {85},
year = {1999}
}
@article{faucris.117901784,
abstract = {We consider optimal control problems related to exact- and approximate controllability of dynamic networks of elastic strings. In this note we concentrate on problems with linear dynamics, no state and no control constraints. The emphasis is on approximating target states and velocities in part of the network using a dynamic domain decomposition method (d(3)m) for the optimality system on the network. The decomposition is established via a Uzawa-type saddle-point iteration associated with an augmented Lagrangian relaxation of the transmission conditions at multiple joints. We consider various cost functions and prove convergence of the infinite dimensional scheme for an exemplaric choice of the cost. We also give numerical evidence in the case of simple exemplaric networks.},
author = {Leugering, Günter},
doi = {10.1023/A:1008721402512},
faupublication = {yes},
journal = {Computational Optimization and Applications},
keywords = {dynamic networks of elastic strings;dynamic domain decomposition;optimal control},
pages = {5-27},
peerreviewed = {Yes},
title = {{Domain} decomposition of optimal control problems for dynamic networks of elastic strings},
url = {http://link.springer.com/article/10.1023/A:1008721402512},
volume = {16},
year = {2000}
}
@article{faucris.111690964,
abstract = {This paper presents a multiobjective search algorithm with subdivision technique (MOSAST) for the global solution of multiobjective constrained optimization problems with possibly noncontinuous objective or constraint functions. This method is based on a random search method and a new version of the Graef-Younes algorithm and it uses a subdivision technique. Numerical results are given for bicriterial test problems. © 2006 Springer Science + Business Media, LLC.},
author = {Jahn, Johannes},
doi = {10.1007/s10589-006-6450-4},
faupublication = {yes},
journal = {Computational Optimization and Applications},
keywords = {Global optimization; Random search; Vector optimization},
note = {UnivIS-Import:2015-03-09:Pub.2006.nat.dma.pama21.multio},
pages = {161-175},
peerreviewed = {Yes},
title = {{Multiobjective} {Search} {Algorithm} with {Subdivision} {Technique}},
volume = {35},
year = {2006}
}
@incollection{faucris.106894304,
address = {Hildesheim},
author = {Rathmann, Wigand and von Schroeders, Nicolai},
booktitle = {Medien im Mathematikunterricht},
editor = {Stephanie Gleich},
faupublication = {yes},
isbn = {978-3-88120-842-0},
pages = {39-56},
peerreviewed = {unknown},
publisher = {Franzbecker},
series = {MaMut Materialien für den Mathematikunterricht},
title = {{Online}-{Auswertungsverfahren} {STACK}},
volume = {6},
year = {2018}
}
@article{faucris.121378444,
abstract = {We present an algorithm for the solution of general inequality constrained optimization problems. The algorithm is based upon an exact penalty function that is approximated by a family of smooth functions. We present convergence results. As numerical examples we treat state constrained optimal control problems for elliptic partial differential equations. We compare the results with existing methods. © 2010 Taylor & Francis.},
author = {Gugat, Martin and Herty, Michael},
doi = {10.1080/10556780903002750},
faupublication = {yes},
journal = {Optimization Methods & Software},
keywords = {Exact penalty function; Optimal control problem; Optimization with partial differential equations},
note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.thesmo},
pages = {573-599},
peerreviewed = {Yes},
title = {{The} smoothed-penalty algorithm for state constrained optimal control problems for partial differential equations},
url = {http://www.informaworld.com/smpp/content~db=all~content=a913030109?words=gugat},
volume = {25},
year = {2010}
}
@inproceedings{faucris.114040784,
author = {Rathmann, Wigand},
booktitle = {7. SAXON SIMULATION MEETING and Mathcad-Workshop},
date = {2015-03-31},
faupublication = {yes},
peerreviewed = {No},
publisher = {TU Chemnitz, Professur für Montage- und Handhabungstechnik},
title = {{Die} {Kettenlinie} als {Kerbgeometrie}},
url = {http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-172556},
venue = {TU Chemnitz},
year = {2015}
}
@article{faucris.202369670,
author = {Keimer, Alexander and Pflug, Lukas},
doi = {10.1016/j.jde.2017.05.015},
faupublication = {yes},
journal = {Journal of Differential Equations},
keywords = {Nonlocal balance law; Existence; Regularity; Nonlocal conservation law; Weak solution; Uniqueness},
pages = {4023-4069},
peerreviewed = {Yes},
title = {{Existence}, uniqueness and regularity results on nonlocal balance laws},
volume = {263},
year = {2017}
}
@incollection{faucris.115535684,
address = {Rocquencourt},
author = {Jahn, Johannes},
booktitle = {Third Franco-German Conference in Optimization},
faupublication = {no},
note = {UnivIS-Import:2015-04-17:Pub.1985.nat.dma.pama21.proper},
pages = {27-28},
peerreviewed = {unknown},
publisher = {INRIA Report},
title = {{Properly} {Minimal} {Elements} of a {Set}},
year = {1985}
}
@article{faucris.107381384,
abstract = {The optimization and manufacturing of an auxetic structure is presented. An inverse homogenization method is used to obtain the optimized geometry shown in the figure. The resulting structure is then produced using selective electron beam melting. The numerically predicted properties are experimentally verifie},
author = {Schwerdtfeger, Jan and Wein, Fabian and Leugering, Günter and Singer, Robert and Körner, Carolin and Stingl, Michael and Schury, F.},
doi = {10.1002/adma.201004090},
faupublication = {yes},
journal = {Advanced Materials},
pages = {2650--2654},
peerreviewed = {Yes},
title = {{Design} of {Auxetic} {Structures} via {Mathematical} {Optimization}},
volume = {23},
year = {2011}
}
@inproceedings{faucris.118501504,
abstract = {We consider the feedback stabilization of quasilinear hyperbolic systems on star-shaped networks. We present boundary feedback controls with varying delays. The delays are given by C
`We consider models based on conservation laws. For the optimization of`

`such systems, a sensitivity analysis is essential to determine how changes in the decision`

`variables influence the objective function. Here we study the sensitivity with respect`

`to the initial data of objective functions that depend upon the solution of Riemann`

`problems with piecewise linear flux functions. We present representations for the one–`

`sided directional derivatives of the objective functions. The results can be used in the`

`numerical method called Front-Tracking.`

International conference on control of distributed parameter systems. 4 (1988)

1989, vol. 91, pp. 249-261 (12 ref.)}, author = {Leugering, Günter}, faupublication = {no}, journal = {International Series of Numerical Mathematics}, month = {Jan}, pages = {249-261}, peerreviewed = {unknown}, title = {{ON} {THE} {REACHABILITY} {PROBLEM} {OF} {A} {VISCOELASTIC} {BEAM} {DURING} {A} {SLEWING} {MANEUVER}}, volume = {91}, year = {1989} } @inproceedings{faucris.106690584, author = {Hante, Falk and Sigalotti, Mario}, booktitle = {Decision and Control (CDC) 2010. CDC 2010, 49th IEEE Conference on}, faupublication = {no}, pages = {5668--5673}, peerreviewed = {unknown}, title = {{Existence} of common {Lyapunov} functions for infinite-dimensional switched linear systems}, year = {2010} } @article{faucris.107052264, abstract = {We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time control applications.}, author = {Langnese, John E. and Leugering, Günter}, doi = {10.1051/cocv:2002042}, faupublication = {no}, journal = {Esaim-Control Optimisation and Calculus of Variations}, keywords = {Maxwell system;optimal control;domain decomposition; 65N55; 49M27; 35Q60}, pages = {775-799}, peerreviewed = {Yes}, title = {{Time} domain decomposition in final value optimal control of the {Maxwell} system}, url = {http://www.esaim-cocv.org/articles/cocv/abs/2002/02/Lagnese/Lagnese.html}, volume = {8}, year = {2002} } @article{faucris.110289344, abstract = {For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H2-Lyapunov function and hence also the H2-norm of the difference between the non-stationary and the stationary state decays exponentially with tim}, author = {Gugat, Martin and Leugering, Günter and Wang, Ke}, doi = {10.3934/mcrf.2017015}, faupublication = {yes}, journal = {Mathematical Control and Related Fields}, keywords = {Boundary feedback control, feedback stabilization, exponential stability, isothermal Euler equations, second-order quasilinear equation, Lyapunov function, stationary state, non-stationary state, gas pipeline}, pages = {419 - 448}, peerreviewed = {Yes}, title = {{Neumann} boundary feedback stabilization for a nonlinear wave equation: {A} strict {H2}-{Lyapunov} function}, volume = {7}, year = {2017} } @article{faucris.119541004, author = {Rathmann, Wigand and Gebald, Christoph}, faupublication = {no}, journal = {Infoplaner}, pages = {36--37}, peerreviewed = {No}, title = {{Grundlagen} {FEM}: {Ritz}-{Verfahren}}, volume = {1/2003}, year = {2003} } @article{faucris.119206604, abstract = {The visual appearance of the artificial world is largely governed by films or composites containing particles with at least one dimension smaller than a micron. Over the past century and a half, the optical properties of such materials have been scrutinized and a broad range of colorant products, based mostly on empirical microstructural improvements, developed. With the advent of advanced synthetic approaches capable of tailoring particle shape, size and composition on the nanoscale, the question of what is the optimum particle for a certain optical property can no longer be answered solely by experimentation. Instead, new and improved computational approaches are required to invert the structure-function relationship. This progress report reviews the development in our understanding of this relationship and indicates recent examples of how theoretical design is taking an ever increasingly important role in the search for enhanced or multifunctional colorants. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.}, author = {Klupp Taylor, Robin and Seifrt, Frantiek and Zhuromskyy, Oleksandr and Peschel, Ulf and Leugering, Günter and Peukert, Wolfgang}, doi = {10.1002/adma.201100541}, faupublication = {yes}, journal = {Advanced Materials}, keywords = {colloids; core/shell nanoparticles; designed nanostructures; functional coatings; structure-property relationships}, pages = {2554-2570}, peerreviewed = {Yes}, title = {{Painting} by numbers: {Nanoparticle}-based colorants in the post-empirical age}, volume = {23}, year = {2011} } @article{faucris.112053744, abstract = {The Lavrentiev regularization method is a tool to improve the regularity of the Lagrange multipliers in pde constrained optimal control problems with state constraints. It has already been used for problems with parabolic and elliptic systems. In this paper we consider Lavrentiev regularization for problems with a hyperbolic system, namely the scalar wave equation. We show that also in this case the regularization yields multipliers in the Hilbert space L

An integrodifferential equation of the Volterra type is considered under the action of an*L*_{2}(0, T, L_{2}(Γ))-boundary control. By harmonic analysis arguments it is shown that the controllability results obtained in [17] for the underlying reference model associated with a trivial convolution kernel, carry over to the model under consideration without any smallness assumption concerning the memory kernel.

}, author = {Leugering, Günter}, doi = {10.1007/BF01442653}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {223-250}, peerreviewed = {Yes}, title = {{EXACT} {BOUNDARY} {CONTROLLABILITY} {OF} {AN} {INTEGRODIFFERENTIAL} {EQUATION}}, url = {http://link.springer.com/article/10.1007/BF01442653}, volume = {15}, year = {1987} } @article{faucris.119702924, abstract = {This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl. Math., vol 3, American Institute of Mathematical Sciences and Higher Education Press, 2010] existing in a neighborhood of the equilibrium solution. The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.}, author = {Leugering, Günter and Li, Tatsien and Gu, Qilong}, doi = {10.1007/s11401-017-1092-7}, faupublication = {yes}, journal = {Chinese Annals of Mathematics. Series B}, keywords = {Exact boundary controllability; Nonlinear Timoshenko beams; Semi-global classical solutions; Tree-like networks}, pages = {711-740}, peerreviewed = {unknown}, title = {{Exact} boundary controllability on a tree-like network of nonlinear planar {Timoshenko} beams}, volume = {38}, year = {2017} } @article{faucris.119402844, abstract = {The feasible set of a convex semi-infinite program is described by a possibly infinite system of convex inequality constraints. We want to obtain an upper bound for the distance of a given point from this set in terms of a constant multiplied by the value of the maximally violated constraint function in this point. Apart from this Lipschitz case we also consider error bounds of Hölder type, where the value of the residual of the constraints is raised to a certain power. We give sufficient conditions for the validity of such bounds. Our conditions do not require that the Slater condition is valid. For the definition of our conditions, we consider the projections on enlarged sets corresponding to relaxed constraints. We present a condition in terms of projection multipliers, a condition in terms of Slater points and a condition in tenus of descent directions. For the Lipschitz case, we give five equivalent characterizations of the validity of a global error bound. We extend previous results in two directions: First, we consider infinite systems of inequalities instead of finite systems. The second point is that we do not assume that the Slater condition holds which has been required in almost all earlier papers. © Springer-Verlag 2000.}, author = {Gugat, Martin}, doi = {10.1007/s101070050016}, faupublication = {no}, journal = {Mathematical Programming}, keywords = {Convex inequalities; Dual solutions; Error bounds; Hölder error bound; Mangasarian-Fromovitz condition; Projection multipliers; Semi-infinite program; Weak slater condition; 20E28; 20G40; 20C20}, note = {UnivIS-Import:2015-03-09:Pub.2000.nat.dma.lama1.errorb}, pages = {255-275}, peerreviewed = {Yes}, title = {{Error} bounds for infinite systems of convex inequalities without {Slater}'s condition}, url = {http://www.springerlink.com/app/home/contribution.asp?wasp=f62clce4kc2rww8fa45u&referrer=parent&backto=issue,3,10;journal,31,44;linkingpublicationresults,id:103081,1}, volume = {88}, year = {2000} } @article{faucris.119924244, abstract = {It is shown that finite energy states of a vibrating viscoelastic plate of the Kelvin-Voigt type are, in general, not exactly controllable by

The number of dual-career couples with children is growing fast. These

couples face various challenging problems of organizing their lifes, in par-

ticular connected with childcare and time-management. As a typical ex-

ample we study one of the difficult decision problems of a dual career

couple from the point of view of operations research with a particular

focus on gender equality, namely the location problem to find a family

home. This leads to techniques that allow to include the value of gender

equality in rational decision processes.

},
author = {Gugat, Martin and Abele-Brehm, Andrea and Klamroth, Kathrin},
faupublication = {yes},
keywords = {Dual Careec couples, Optimal Location Problem, Childcare Management},
peerreviewed = {automatic},
title = {{Optimal} location of family homes for dual career couples},
url = {http://www.optimization-online.org/DB_HTML/2010/02/2547.html},
year = {2010}
}
@article{faucris.115105144,
abstract = {In this paper the problem dual to a convex vector optimization problem is defined. Under suitable assumptions, a weak, strong and strict converse duality theorem are proved. In the case of linear mappings the formulation of the dual is refined such that well-known dual problems of Gale, Kuhn and Tucker [8] and Isermann [12] are generalized by this approach. © 1983 The Mathematical Programming Society, Inc.},
author = {Jahn, Johannes},
doi = {10.1007/BF02594784},
faupublication = {no},
journal = {Mathematical Programming},
keywords = {Duality; Vector Optimization},
note = {UnivIS-Import:2015-03-05:Pub.1983.nat.dma.pama21.dualit},
pages = {343-353},
peerreviewed = {Yes},
title = {{Duality} in {Vector} {Optimization}},
volume = {25},
year = {1983}
}
@inproceedings{faucris.123961684,
author = {Rathmann, Wigand},
booktitle = {5. SAXON SIMULATION MEETING and Mathcad-Workshop},
date = {2013-04-22/2013-04-23},
faupublication = {yes},
keywords = {Massenschwinger, quadratische Formen, Ingenieurmathematik},
peerreviewed = {No},
publisher = {TU Chemnitz, Professur für Montage- und Handhabungstechnik},
title = {{Eigenwerte} und {Fourier} - {Simulation} von {Massenschwingern} mit {Mathcad}},
url = {http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-114465},
venue = {TU Chemnitz},
year = {2013}
}
@article{faucris.118517124,
abstract = {In this contribution the identification of new reaction conditions for the production of nearly monodisperse silicon nanoparticles via the pyrolysis of monosilane in a hot wall reactor is considered. For this purpose a full finite volume model has been combined with a state-of-the-art trust-region optimisation algorithm for process control. Verified against experimental data, specific process conditions are determined accomplishing a versatile range of prescribed product properties. The main achievement of the optimisation is the possibility to control the different mechanisms in the particle formation process by mainly adjusting the temperature profile. Due to a successful separation of the nucleation and growth process, significantly narrower particle size distributions are obtained. Moreover, the presented optimisation framework establishes rate constants based on measured data.},
author = {Gröschel, Michael and Koermer, Richard and Walther, Maximilian and Leugering, Günter and Peukert, Wolfgang},
doi = {10.1016/j.ces.2012.01.035},
faupublication = {yes},
journal = {Chemical Engineering Science},
pages = {181--194},
peerreviewed = {Yes},
title = {{Process} control strategies for the gas phase synthesis of silicon nanoparticles},
volume = {73},
year = {2012}
}
@incollection{faucris.117917844,
address = {New York, Basel, Hong Kong},
author = {Langnese, John E. and Leugering, Günter},
booktitle = {Differential Equations with Applications in Biology, Physics, and Engineering},
editor = {Jerome A. Goldstein, Franz Kappel, Wilhelm Schappacher},
faupublication = {no},
isbn = {0-8247-8571-1},
month = {Jan},
pages = {227-239},
peerreviewed = {unknown},
publisher = {Marcel Dekker, Inc.},
series = {A Series of Lecture Notes in Pure and Applied Mathematics},
title = {{UNIFORM} {ENERGY} {DECAY} {OF} {A} {CLASS} {OF} {CANTILEVERED} {NONLINEAR} {BEAMS} {WITH} {NONLINEAR} {DISSIPATION} {AT} {THE} {FREE} {END}},
volume = {133},
year = {1991}
}
@article{faucris.117907504,
abstract = {We consider an elliptic distributed quadratic optimal control problem with exact controllability constraints on a part of the domain which, in turn, is parametrized by a small parameter e. The quadratic tracking type functional is defined on the remaining part of the domain. We thus consider a family of optimal control problems with state equality constraints. The purpose of this paper is to study the asymptotic limit of the optimal control problems as the parameter e tends to zero. The analysis presented is in the spirit of the direct approach of the calculus of variations. This is achieved in the framework of relaxed problems. We finally apply the procedure to an optimal control problem on a perforated domain with holes of critical size. It is shown that a strange term in the terminology of Cioranescu and Murat (Prog. Nonlinear Diff. Eq. Appl., Vol. 31, Birkhauser-Verlag, Boston, 1997, pp. 49-93) appears in the limiting homogenized problem.},
author = {Kogut, Peter I. and Leugering, Günter},
doi = {10.3233/ASY-2008-0871},
faupublication = {yes},
journal = {Asymptotic Analysis},
keywords = {controllability constraints;relaxed problems;gamma(Delta) and Gamma-convergence;perforated domains},
month = {Jan},
pages = {229-249},
peerreviewed = {Yes},
title = {{Homogenization} of {Dirichlet} optimal control problems with exact partial controllability constraints},
url = {http://content.iospress.com/articles/asymptotic-analysis/asy871},
volume = {57},
year = {2008}
}
@article{faucris.118529664,
abstract = {In this paper we study a Dirichlet optimal control problem associated with a linear elliptic equation the coefficients of which we take as controls in L (Ω). In particular, when the coefficient matrix is taken to satisfy the decomposition B(x) = ρ(x)A(x) with a scalar function ρ, we allow the ρ to degenerate. Such problems are related to various applications in mechanics, conductivity and to an approach in topology optimization, the SIMP-method. Since equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we show that the optimal control problem in the coefficients can be stated in different forms depending on the choice of the class of admissible solutions. Using the direct method in the Calculus of variations, we discuss the solvability of the above optimal control problems in the so-called class of H-admissible solutions. © European Mathematical Society.},
author = {Kogut, Peter I. and Leugering, Günter},
doi = {10.4171/ZAA/1447},
faupublication = {yes},
journal = {Zeitschrift für Analysis und ihre Anwendungen},
keywords = {Degenerate elliptic equations;control in coefficients;weighted Sobolev spaces;Lavrentieff phenomenon;direct method in the Calculus of variations},
month = {Jan},
pages = {31--53},
peerreviewed = {Yes},
title = {{Optimal} {L1}-{Control} in {Coefficients} for {Dirichlet} {Elliptic} {Problems}: {H}-{Optimal} {Solutions}},
volume = {31},
year = {2012}
}
@article{faucris.122597244,
abstract = {Dielectric-metal core-shell particles with morphologically tunable optical properties are highly promising candidates for applications ranging from theranostics, energy harvesting and storage to pigments and sensors. Most structures of interest have, until now, been produced in small volume wet chemical batch approaches which are difficult to scale. In extension to the growing interest in continuous flow process for the scalable synthesis of single phase nanomaterials, here we describe the formation of two-phase core-shell particles. Specifically, the coating of silver onto colloidal silica particles using a static T-mixer approach is presented. The coating is achieved in a single reaction step in which careful control of educt concentration and process conditions leads to nucleation and surface conformal growth of silver. Through two generations of reactor, good coating yield and process reproducibility are demonstrated. In particular, the ability to control the characteristic time of mixing, as verified by the Villermaux-Dushmann reaction, was shown to be crucial in narrowing the range of morphologies obtained in the product particles. Moreover we could tune, through process parameters, the degree of coating of the core particles, leading to patchy particles, Janus particles and even complete nanoshells. Since silver nanostructures have a strong structure-dependent plasmon resonance, we could verify the coating morphologies via optical spectroscopy and electrodynamic simulations. Optical measurements were also used in order to optimize, via trial and error, the continuous flow process parameters to produce a high coating yield. This opens up future potential for feedback-driven optimization of particle coating. Finally, we demonstrate that the silver coatings can be morphologically stabilized, opening up the possibility of effective formulation for applications.},
author = {Meincke, Thomas and Bao, Huixin and Pflug, Lukas and Stingl, Michael and Klupp Taylor, Robin},
doi = {10.1016/j.cej.2016.09.048},
faupublication = {yes},
journal = {Chemical Engineering Journal},
keywords = {Continuous flow nanoparticle synthesis; Diffusion limited growth; Metal nanoshell; Microreactor; Patchy particle; Plasmon resonance},
pages = {89-100},
peerreviewed = {Yes},
title = {{Heterogeneous} nucleation and surface conformal growth of silver nanocoatings on colloidal silica in a continuous flow static {T}-mixer},
volume = {308},
year = {2017}
}
@incollection{faucris.118886284,
address = {Boston},
author = {Jahn, Johannes},
booktitle = {Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications},
editor = {T. Gal, T.J. Stewart, T. Hanne},
faupublication = {yes},
note = {UnivIS-Import:2015-04-20:Pub.1999.nat.dma.pama21.theory},
pages = {2-1 - 2-32},
peerreviewed = {unknown},
publisher = {Kluwer},
title = {{Theory} of {Vector} {Maximization}: {Various} {Concepts} of {Efficient} {Solutions}},
year = {1999}
}
@article{faucris.117420424,
abstract = {We investigate the evolution and propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. In addition to the classical variational formulation, where the standard potential energy is minimized over the cracked domain under physical conditions characterizing the behavior of the material close to the crack (e.g. non-penetration conditions), we include a 'cohesive traction term' in the energy expression. In this way we obtain a mathematically concise set of partial differential equations with non-linear boundary conditions at the crack interfaces. We perform a finite element discretization using a combination of standard continuous finite elements and so-called cohesive elements. During the simulation process cohesive elements are adaptively inserted at positions where a certain stress bound is exceeded. In our numerical studies we consider domains consisting of a matrix material with fiber inclusions. Beyond pure crack path simulation, our ultimate goal is to determine an optimal shape of the fibers resulting in a crack path that releases for a given load scenario as much energy as possible without destroying the specimen completely. We develop a corresponding optimization model and propose a solution algorithm for the same. The article is concluded by numerical results. © 2011 Elsevier Ltd.},
author = {Prechtel, Marina and Leugering, Günter and Steinmann, Paul and Stingl, Michael},
doi = {10.1016/j.engfracmech.2011.01.007},
faupublication = {yes},
journal = {Engineering Fracture Mechanics},
keywords = {Cohesive zone modeling; Crack growth; Fiber reinforced material; Shape optimization},
note = {UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.toward},
pages = {944-960},
peerreviewed = {Yes},
title = {{Towards} optimization of crack resistance of composite materials by adjustment of fiber shapes},
volume = {78},
year = {2011}
}
@article{faucris.107392824,
abstract = {For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H-2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H-2-Lyapunov function and hence also the H-2-norm of the difference between the non-stationary and the stationary state decays exponentially with time.},
author = {Leugering, Günter and Gugat, Martin and Wang, Ke},
doi = {10.3934/mcrf.2017015},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Boundary feedback control;feedback stabilization;exponential stability;isothermal Euler equations;second-order quasilinear equation;Lyapunov function;stationary state;non-stationary state;gas pipeline},
pages = {419-448},
peerreviewed = {Yes},
title = {{NEUMANN} {BOUNDARY} {FEEDBACK} {STABILIZATION} {FOR} {A} {NONLINEAR} {WAVE} {EQUATION}: {A} {STRICT} {H}-2-{LYAPUNOV} {FUNCTION}},
volume = {7},
year = {2017}
}
@article{faucris.115130224,
abstract = {Pipeline networks for gas transportation often contain circles. For such networks it is more difficult to determine the stationary states than for networks without circles. We present a method that allows to compute the stationary states for subsonic pipe flow governed by the isothermal Euler equations for certain pipeline networks that contain circles. We also show that suitably chosen boundary data determine the stationary states uniquely. The construction is based upon novel explicit representations of the stationary states on single pipes for the cases with zero slope and with nonzero slope. In the case with zero slope, the state can be represented using the Lambert-W function.},
author = {Gugat, Martin and Hante, Falk and Hirsch-Dick, Markus and Leugering, Günter},
doi = {10.3934/nhm.2015.10.295},
faupublication = {yes},
journal = {Networks and Heterogeneous Media},
keywords = {Network;isothermal Euler equations;stationary state;circles;cycles;gas transportation network},
pages = {295-320},
peerreviewed = {Yes},
title = {{STATIONARY} {STATES} {IN} {GAS} {NETWORKS}},
volume = {10},
year = {2015}
}
@article{faucris.201251594,
author = {Gugat, Martin and Wintergerst, David},
doi = {10.2478/amcs-2018-0025},
faupublication = {yes},
journal = {International Journal of Applied Mathematics and Computer Science},
pages = {341–348},
peerreviewed = {Yes},
title = {{Transient} flow in gas networks: {Traveling} waves},
url = {https://www.amcs.uz.zgora.pl/?action=paper&paper=1434},
volume = {28},
year = {2018}
}
@inproceedings{faucris.121391204,
address = {Aachen},
author = {Jahn, Johannes and Rathje, U.},
booktitle = {Multicriteria Decision Making and Fuzzy Systems - Theory, Methods and Applications},
editor = {K.H. Küfer, H. Rommelfanger, C. Tammer, K. Winkler},
faupublication = {yes},
note = {UnivIS-Import:2015-04-16:Pub.2006.nat.dma.pama21.graefy},
pages = {75 - 81},
peerreviewed = {unknown},
publisher = {Shaker Verlag},
title = {{Graef}-{Younes} {Method} with {Backward} {Iteration}},
year = {2006}
}
@article{faucris.124098084,
abstract = {We present a compact overview of the recent development in free material optimization (FMO), a branch of structural optimization. The goal of FMO is to design the ultimately best material (its mechanical properties and distribution in space) for a given purpose. We show that the current FMO models naturally lead to linear and non-linear semidefinite programming problems (SDP); their numerical tractability is then guaranteed by recently introduced SDP algorithms.},
author = {Kocvara, Michal and Stingl, Michael and Zowe, Jochem},
doi = {10.1080/02331930701778908},
faupublication = {yes},
journal = {Optimization},
keywords = {optimization of elastic structures;material optimization;topology optimization;semidefinite programming;method of augmented Lagrangians},
pages = {79-100},
peerreviewed = {Yes},
title = {{Free} material optimization: recent progress},
volume = {57},
year = {2008}
}
@article{faucris.117908604,
abstract = {We consider the optimal control problems for the linear elliptic equations in perforated domains. Each components of mathematical description of such optimal control problem depends on small parameter epsilon. Problems of this type appear in sensitivity analysis, perturbation theory, and homogenization of heterogenous material. We study the problem of passing to the limit within the framework of variational S-convergence. We derive conditions under which the so-called fictitious limiting optimal control problem can be made explicit.},
author = {Kogut, Peter I. and Leugering, Günter},
faupublication = {no},
journal = {Asymptotic Analysis},
keywords = {homogenization; S-convergence; optimal control; variable domains},
pages = {37-72},
peerreviewed = {Yes},
title = {{Homogenization} of optimal control problems in variable domains. {Principle} of the fictitious homogenization},
url = {http://content.iospress.com/articles/asymptotic-analysis/asy438},
volume = {26},
year = {2001}
}
@article{faucris.113245924,
abstract = {In the semianalytical models for squeeze film damping, the coefficient of damping torque is expressed as an infinite double series. To work with these models, methods for the efficient numerical evaluation of these double series are important, because, as has been pointed out, the results are given by complicated equations; the application of the results is difficult. This paper presents a transformation of the equations that allows a fast and reliable numerical evaluation of the coefficient of damping torque for torsion mirrors.We give precise error bounds and present examples that illustrate that approximations with one or two terms are often sufficient in practice. © 2013 American Society of Civil Engineers.},
author = {Gugat, Martin},
doi = {10.1061/(ASCE)NM.2153-5477.0000075},
faupublication = {yes},
journal = {Journal of Nanomechanics and Micromechanic},
keywords = {Approximation of the coefficient of damping torque; Coefficient of damping torque; Efficient computation of double series; Error bound; Squeeze film damping},
note = {UnivIS-Import:2015-03-09:Pub.2013.nat.dma.lama1.effici},
peerreviewed = {Yes},
title = {{Efficient} {Numerical} {Evaluation} of {Semianalytical} {Models} for {Squeeze} {Film} {Damping} for {Torsion} {Mirrors}},
url = {http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29NM.2153-5477.0000075},
volume = {3},
year = {2013}
}
@incollection{faucris.119669264,
abstract = {We present an overview on recent results concerning hyperbolic systems on networks. We present a summary of theoretical results on existence, uniqueness and stability. The established theory extends previously known results on the Cauchy problem for nonlinear, 2The LMS Moodle and ILIAS are widely used at universities and Universities of Applied

Sciences. But even nowadays, it is still a challenge to use the possibilities given by digital

materials to create learning content which offers more than a classical textbook. Several

tools are available to show, explain and dynamically explore mathematical concepts,

among them are CoCalc (former SageMathCloud), SageCell, CDF-Player, JSXGraph and

GeoGebra. It is still quite common that content for a lecture is provided inside the local

LMS, while the learner has to open another platform or software to use the dynamic

mathematical tools for exploration of the content. In our contribution (talk or poster) we

will show our approaches to include dynamic mathematics inside LMS.

In particular, we use JSXGraph for dynamic 2D diagrams and the SageMathCell for a wide

range of mathematical aspects. JSXGraph is a JavaScript library, which is quite easy to use

and which offers the possibility to include user interactions via HTML-forms. The

advantage is that the computations are done in the browser on client-side. On the other

hand, SageMathCell has a huge variety of tools already included, like Maxima, R, Octave

or Python. Furthermore, it is very easy to show 3D-diagrams. This is made possible by

executing the computation on a remote server, which has to be connected from the content.

We include JSXGraph and SageMathCell in classical HTML-Pages as media content and

through dedicated plug-ins for the LMS Moodle and ILIAS. During the ”Mathematics for

Engineers” (part 1-3) we provide additional material for several topics, e.g. series, (un)-

constrained optimization, integration, parametrization of curves and surfaces or differential

equations. We see the advantage that the diagrams will become an integral part of the

learning modules and the learning unit does not look like patchwork.

Further, the learners can focus on the content and do not have to bring additional software

or to login in a second learning platform. During presence lectures the lecturer can use the

same LMS as the learnersdo for their follow-up work.

For JSXGraph, there is a plug-in for Moodle, for the usage of SageMathCell inside ILIAS

the first author could initiate the development.

1-solutions. There are no restrictions on the distance between the initial state and the target state, so our result is a global controllability result for a nonlinear hyberbolic system. © 2003 Éditions scientifiques et médicales Elsevier SAS.}, author = {Leugering, Günter and Gugat, Martin}, doi = {10.1016/S0294-1449(02)00004-5}, faupublication = {yes}, journal = {Annales de l'Institut Henri Poincaré - Analyse Non Linéaire}, keywords = {Characteristic form; de St. Venant equation; Global controllability; Nonlinear hyperbolic system}, note = {UnivIS-Import:2015-03-09:Pub.2003.nat.dma.lama1.global}, pages = {1-11}, peerreviewed = {Yes}, title = {{Global} boundary controllability of the de {St}. {Venant} equations between steady states}, volume = {20}, year = {2003} } @article{faucris.121727144, abstract = {The practice of production of composite materials with thin fibers requires a correct description of problems of the equilibrium of elastic bodies containing thin rigid inclusions. Of large importance is also an adequate description of the interaction of thin inclusions with cracks in an elastic body. As is known, inclusions can delaminate from the matrix, thereby forming a crack in the elastic body. A traditional approach to the description of cracks in elastic bodies consists in the use of equality-type boundary conditions at the crack faces. This approach frequently leads to unphysical results; for example, the corresponding solutions can yield a mutual penetration of the crack faces (see, e.g., [1, 2]). In the recent years, there was performed a wide cycle of investigations in the theory of cracks with boundary conditions corresponding to the mutual nonpenetration of the crack edges. In this case, the boundary conditions at the crack faces have the form of a set of equalities and inequalities. For acquaintance with such models, one can turn to [3, 4], where numerous appropriate references can be found. In this works, we suggest a model of an elastic body containing thin rigid inclusions with a property of delamination. For describing the delamination, we use inequality-type boundary conditions eliminating the mutual penetration of the crack faces.}, author = {Leugering, Günter and Khludnev, A. M.}, doi = {10.1134/S1028335810010040}, faupublication = {yes}, journal = {Doklady Physics}, pages = {18--22}, peerreviewed = {Yes}, title = {{On} the equilibrium of elastic bodies containing thin rigid inclusions}, volume = {55}, year = {2010} } @phdthesis{faucris.106824124, abstract = {We study the shallow water equations augmented with pollution transport in one space dimension on prismatic channels with nontrivial channel width. We use both, the characteristic and the weak formulation, to construct an explicit solution of the corresponding Riemann problem. This solution is an important ingredient for Godunov's Finite volume scheme, which is used to discretize a real world sewer system into a network of finite volume elements. We especially focus on a finite volume model for the network vertices, which implies weak coupling conditions at each vertex and is based on the solution of a transjunctional Riemann problem. In order to develop a process model for sewer systems of practical relevance, we introduce generalized numerical flux functions, which allow the modeling of wave reflections at nonprismatic channel junctions and walls. The generalized numerical flux functions also enable the modeling of controllable special structures like pumps, weirs and valves. The resulting process model is especially suited for real world sewer systems and is mathematically represented by a system of ordinary differential equations. The controllable process model is subject to an optimal control problem for real-time application. We discretize the process model with a general linear one-step scheme in time and use adjoint calculus to provide explicit formulas for the gradient and Hessian of the time discrete cost functional. We verify our approach with a self-written C++ application, which is tailored to optimize finite volume networks in real-time, and provide numerical results for two sewer systems, which are both based on practical application. We apply a receding horizon strategy to both test cases and compare the real-time control results with the previously computed solutions of an online control approach.}, author = {Hild, Johannes}, faupublication = {yes}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Real}-{Time} {Control} of {Hydrodynamic} {Process} {Models} on {Finite} {Volume} {Networks}}, year = {2012} } @article{faucris.112679424, abstract = {We consider a water distribution network where at a finite number of nodes, contaminant injection can occur. We consider the problem of the identification of the contaminations. This problem can be considered as an optimal control problem with a networked system that is governed by a transport reaction equation. The identification is based upon observations from a finite number of sensors. The corresponding infinite-dimensional optimization problem is defined in a Hilbert space setting. In order to guarantee that our optimization problem has a unique solution, a quadratic regularization term is added in the objective function. Under certain assumptions on the relations of the travel times through the pipes we obtain a representation of this optimization problem that allows the computation of the solution on a discrete time grid by solving finite-dimensional linear least squares problems. On these time grids, there is no discretization error since our approach is based upon an exact representation of the system state. This is useful to minimize potential impacts of contamination emergencies on consumers by helping to select locations to flush the contaminant out of the distribution network. © 2012 Society for Industrial and Applied Mathematics.}, author = {Gugat, Martin}, doi = {10.1137/110859269}, faupublication = {yes}, journal = {SIAM Journal on Applied Mathematics}, keywords = {Contamination emergency; Hyperbolic PDE; Identification; Least squares; Network; Network dynamics; Observation; Optimal control; PDE-constrained optimization; Transport reaction equation}, note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.lama1.contam}, pages = {1772-1791}, peerreviewed = {Yes}, title = {{Contamination} {Source} {Determination} in {Water} {Distribution} {Networks}}, url = {http://epubs.siam.org/doi/abs/10.1137/110859269}, volume = {72}, year = {2012} } @incollection{faucris.117911464, abstract = {We consider a planar graph representative of the reference configuration of a network of elastic prestretched strings coupled at the vertices of that graph. Some or all of the vertices may carry a point mass, and at those nodes dry friction on the plane may occur. We briefly describe the model and some results on well-posedness and control of such systems obtained in the literature. We then introduce a dynamic domain decomposition based on a Steklov-Poincaré-type operator. The analysis is given for the time-domain and the frequency-domain. Optimal control and problems of exact controllability are formulated and investigated in terms of the decoupling procedure.}, address = {Basel}, author = {Leugering, Günter}, booktitle = {Control and Estimation of Distributed Parameter Systems - International Conference in Vorau, Austria, July 14-20, 1996}, doi = {10.1007/978-3-0348-8849-3_15}, editor = {W. Desch; F. Kappel; K. Kunisch}, faupublication = {no}, isbn = {978-3-0348-8849-3}, keywords = {dynamic domain decomposition;strings;networks;joint masses;dry friction;Steklov-Poincare-operators for networks;differential-delay systems;optimal control;controllability; 93C20; 93C80; 93B05; 65N55}, month = {Jan}, pages = {191-205}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {International Series of Numerical Mathematics}, title = {{On} dynamic domain decomposition of controlled networks of elastic strings and joint-masses}, url = {http://link.springer.com/chapter/10.1007/978-3-0348-8849-3_15}, volume = {126}, year = {1998} } @article{faucris.222304913, author = {Geiger, Manfred and Meßner, Arthur and Engel, Ulf}, faupublication = {yes}, journal = {Production Engineering}, note = {LFT Import::2019-07-15 (650)}, peerreviewed = {Yes}, title = {{Production} of microparts - size effects in bulk metal {Forming}, similarity theory.}, year = {1996} } @article{faucris.112240964, abstract = {In this paper, we first define a T-cone which is a unified version of several cones, namely, contingent cone, radial cone, C-tangent cone, Clarke tangent cone, S-cone, adjacent cone, etc. Then, we define the T-epiderivative of a set-valued map which includes the contingent epiderivative, radial epiderivative, S-epiderivative, adjacent epiderivative etc. as special cases. We present several properties of such an epiderivative. The generalized vector T-variational inequality problem is also considered. We provide necessary and sufficient conditions for a solution of a set optimization problem. Several existence results for solutions of set optimization problems and a generalized vector T-variational inequality problem are given.}, author = {Jahn, Johannes and Ansari, Q.H.}, faupublication = {yes}, journal = {Taiwanese Journal of Mathematics}, keywords = {Contingent epiderivative; Existence results; Generalized vector t-variational inequality problems; Optimality conditions; Radial epiderivative; Sepiderivative; T-cone; T-epiderivative; Vector optimization problem}, note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.pama21.tepide}, pages = {2447-2468}, peerreviewed = {Yes}, title = {{T}-epiderivatives of set-valued maps and its application to set optimization and generalized variational inequalities}, volume = {14}, year = {2010} } @article{faucris.117696964, author = {Domschke, Pia and Groß, Martin and Hante, Falk and Hiller, Benjamin and Schewe, Lars and Schmidt, Martin}, faupublication = {yes}, journal = {Gas und Wasserfach, Gas, Erdgas}, pages = {880-885}, peerreviewed = {No}, title = {{Mathematische} {Modellierung}, {Simulation} und {Optimierung} von {Gastransportnetzwerken}}, url = {https://www.di-verlag.de/de/Zeitschriften/gwf-Gas-Erdgas/2015/11/Mathematische-Modellierung-Simulation-und-Optimierung-von-Gastransportnetzwerken}, volume = {156}, year = {2015} } @incollection{faucris.116884504, abstract = {We consider a network where a dynamical process governed by hyperbolic conservation laws takes place. At the vertices, the conservation laws are coupled by algebraic node conditions. The system is also controlled at the vertices through these conditions. To solve problems of optimal control for such a system, an adjoint sensitivity calculus is useful since it allows the efficient evaluation of the gradient of the objective function. We present such a calculus in the framework of classical solutions.}, address = {Boca Raton}, author = {Gugat, Martin}, booktitle = {Control and Boundary Analysis}, editor = {John Cagnol and Jean-Paul Zolesio}, faupublication = {yes}, keywords = {Sensitivy calculus, adkoint system}, note = {UnivIS-Import:2015-04-20:Pub.2005.nat.dma.lama1.nodalc}, pages = {201-214}, peerreviewed = {Yes}, publisher = {Chapman & Hall/CRC Press}, series = {Pure and Applied Mathematics}, title = {{Nodal} {Control} of {Conservation} {Laws} on {Networks}}, volume = {240}, year = {2005} } @article{faucris.217952993, abstract = {In this paper, we study a nonlinear Caputo fractional boundary value problem on a star graph. By means of transformation, an equivalent system of fractional boundary value problem is obtained. Then we establish the existence and uniqueness results by fixed point theory: in particular, using Banach's contraction principle and Schaefer's fixed point theorem. We also present some examples to illustrate the application of our results.}, author = {Mehandiratta, Vaibhav and Mehra, Mani and Leugering, Günter}, doi = {10.1016/j.jmaa.2019.05.011}, faupublication = {yes}, journal = {Journal of Mathematical Analysis and Applications}, keywords = {Boundary value problem; Caputo fractional derivative; Differential equation on graphs; Fixed point theorems}, note = {CRIS-Team Scopus Importer:2019-05-21}, peerreviewed = {Yes}, title = {{Existence} and uniqueness results for a nonlinear {Caputo} fractional boundary value problem on a star graph}, year = {2019} } @article{faucris.110301884, abstract = {In this paper, a known scalarization result of vector optimization theory is reviewed and stated in a different form and a new short proof is presented. Moreover, it is shown how to apply this result to multi-objective optimization problems and to special problems in statistics and optimal control theory. © 1987 Plenum Publishing Corporation.}, author = {Jahn, Johannes}, doi = {10.1007/BF00940199}, faupublication = {yes}, journal = {Journal of Optimization Theory and Applications}, keywords = {control approximation; covariance matrices; Multi-objective optimization}, note = {UnivIS-Import:2015-03-05:Pub.1987.nat.dma.pama21.parame}, pages = {503-516}, peerreviewed = {Yes}, title = {{Parametric} {Approximation} {Problems} {Arising} in {Vector} {Optimization}}, volume = {54}, year = {1987} } @misc{faucris.123719024, author = {Jahn, Johannes}, faupublication = {no}, peerreviewed = {automatic}, title = {{Vektoroptimierung} und deren {Anwendung} in der {Approximations}- und {Steuerungstheorie}}, year = {1983} } @article{faucris.110992904, abstract = {

We consider *L* ^{∞}-norm minimal controllability problems for vibrating systems. In the common method of modal truncation controllability constraints are first reformulated as an infinite sequence of moment equations, which is then truncated to a finite set of equations. Thus, feasible controls are represented as solutions of moment problems.

In this paper, we propose a different approach, namely to replace the sequence of moment equations by a sequence of moment inequalities. In this way, the feasible set is enlarged. If a certain relaxation parameter tends to zero, the enlarged sets approach the original feasible set. Numerical examples illustrate the advantages of this new approach compared with the classical method of moments.

The introduction of moment inequalities can be seen as a regularization method, that can be used to avoid oscillatory effects. This regularizing effect follows from the fact that for each relaxation parameter, the whole sequence of eigenfrequencies is taken into account, whereas in the method of modal truncation, only a finite number of frequencies is considered.

}, author = {Gugat, Martin and Leugering, Günter}, doi = {10.1023/A:1015472323967}, faupublication = {no}, journal = {Computational Optimization and Applications}, keywords = {optimal control; exact controllability; eigenvalues; moment problem; moment inequalities; numerical algorithm; convergence}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.regula}, pages = {151-192}, peerreviewed = {Yes}, title = {{Regularization} of {L}-∞ optimal control problems for distributed parameter systems}, url = {http://link.springer.com/article/10.1023/A:1015472323967}, volume = {22}, year = {2002} } @misc{faucris.115699584, author = {Geißler, Björn and Kolb, Oliver and Lang, Jens and Leugering, Günter and Martin, Alexander and Morsi, Antonio}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Mixed} {Integer} {Linear} {Models} for the {Optimization} of {Dynamical} {Transport} {Networks}}, year = {2010} } @article{faucris.115874264, abstract = {For p is not 2, only few results abaout analytic solutions of problems of optimal control of distributed parameter systems with LP-norm have been reported in the literature. In this paper we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. The aim is to steer the system from a position of rest to a constant terminal state in a given finite time. Also more general final configurations are considered.
The objective function that is to be minimized is the maximum of the L-p-norms of the control functions at both boundaries. It is shown that the analytic solution is, in fact, independent of the choice of the p norm that is minimized. So the optimal controls solve a problem of multicriteria optimization, with the L-p-norms as objective functions.},
author = {Gugat, Martin and Leugering, Günter},
faupublication = {yes},
journal = {Computational and Applied Mathematics},
keywords = {optimal control;wave equation;analytic solution;distributed parameter systems;boundary control;robust control; 90C31; 90C34; 49K40},
month = {Jan},
note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.soluti},
pages = {227-244},
peerreviewed = {Yes},
title = {{Solutions} of {L}-p-norm-minimal control problems for the wave equation},
volume = {21},
year = {2002}
}
@incollection{faucris.121574244,
address = {Berlin},
author = {Jahn, Johannes},
booktitle = {Operations Research Proceedings 1983},
editor = {H. Steckhan, W. Bühler, K.-E. Jäger, Ch. Schneeweiß, J. Schwarze},
faupublication = {no},
note = {UnivIS-Import:2015-04-17:Pub.1984.nat.dma.pama21.neuere},
pages = {511-519},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Neuere} {Entwicklungen} in der {Vektoroptimierung}},
year = {1984}
}
@article{faucris.123049784,
abstract = {A viscoelastic liquid confined between two parallel plates is considered under the action of *L*_{2} (*O, T*)-boundary controls. Applying Laplace-Transform-techniques it is shown that *L*_{2} (*O, l*)-states are exactly controllable in finite time, depending on the speed of propagation of singularities. Finally the existence of time-optimal controls respecting a given norm bound is shown.},
author = {Leugering, Günter},
doi = {10.1002/mma.1670090130},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
month = {Jan},
pages = {413-430},
peerreviewed = {Yes},
title = {{TIME} {OPTIMAL} {BOUNDARY} {CONTROLLABILITY} {OF} {A} {SIMPLE} {LINEAR} {VISCOELASTIC} {LIQUID}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670090130/full},
volume = {9},
year = {1987}
}
@article{faucris.117724244,
abstract = {We consider the problem of boundary feedback stabilization of a vibrating string that is fixed at one end and with control action at the other end. In contrast to previous studies that have required L^{2}-regularity for the initial position and H^{-1}-regularity for the initial velocity, in this paper we allow for initial positions with L^{1}-regularity and initial velocities in W^{-1, 1} on the space interval. It is well known that for a certain feedback parameter, for sufficiently regular initial states the classical energy of the closed-loop system with Neumann velocity feedback is controlled to zero after a finite time that is equal to the minimal time where exact controllability holds. In this paper, we present a Dirichlet boundary feedback that yields a well-defined closed-loop system in the (L^{1}, W^{-1,1}) framework and also has this property. Moreover, for all positive feedback parameters our feedback law leads to exponential decay of a suitably defined L^{1}-energy. For more regular initial states with (L^{2}, H^{-1}) regularity, the proposed feedback law leads to exponential decay of an energy that corresponds to this framework. If the initial states are even more regular with H^{1}-regularity of the initial position and L^{2}-regularity of the initial velocity, our feedback law also leads to exponential decay of the classical energy.},
author = {Gugat, Martin},
doi = {10.1137/140977023},
faupublication = {yes},
journal = {SIAM Journal on Control and Optimization},
keywords = {Dirichlet boundary control; Energy decay; Exact control; Exponential stability; Vibrating string},
note = {UnivIS-Import:2015-03-11:Pub.2015.nat.dma.zentr.expone},
pages = {526-546},
peerreviewed = {Yes},
title = {{EXPONENTIAL} {STABILIZATION} {OF} {THE} {WAVE} {EQUATION} {BY} {DIRICHLET} {INTEGRAL} {FEEDBACK}},
volume = {53},
year = {2015}
}
@article{faucris.114041664,
author = {Rathmann, Wigand and Krug, Andreas},
faupublication = {no},
journal = {Infoplaner},
pages = {36--37},
peerreviewed = {No},
title = {{Grundlagen} {FEM}: {Finite}-{Differenzen}-{Verfahren}},
year = {2004}
}
@article{faucris.112052644,
abstract = {We consider a sloped canal with friction that is governed by the Saint-Venant system with source term. We show that starting sufficiently close to a stationary constant subcritical initial state, we can control the system in finite time to a state in a C^{1} neighbourhood of any other stationary constant subcritical state by boundary control at the ends of the canal in such a way that during the process the system state remains continuously differentiable. Moreover, we show that if the derivative of the initial state is sufficiently small, it can be steered to every stationary constant subcritical state in finite time. © 2008.},
author = {Gugat, Martin and Leugering, Günter},
doi = {10.1016/j.anihpc.2008.01.002},
faupublication = {yes},
journal = {Annales de l'Institut Henri Poincaré - Analyse Non Linéaire},
keywords = {Friction; Global controllability; Nonlinear hyperbolic system; Saint-Venant equation; Slope; Source term},
note = {UnivIS-Import:2015-03-09:Pub.2009.nat.dma.zentr.global},
pages = {257-270},
peerreviewed = {Yes},
title = {{Global} boundary controllability of the {Saint}-{Venant} system for sloped canals with friction},
url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VKB-4RR8YX6-1&_user=616145&_coverDate=02%2F01%2F2008&_alid=714774454&_rdoc=1&_fmt=summary&_orig=search&_cdi=6118&_sort=d&_docanchor=&view=c&_ct=2&_acct=C000032322&_version=1&_urlVersion=0&_userid=616145&md5=31e90bfd85a87331d01e34c56914fa42},
volume = {26},
year = {2009}
}
@article{faucris.122296724,
abstract = {In optimal control loops delays can occur, for example through transmission via digital communication channels. Such delays influence the state that is generated by the implemented control. We study the effect of a delay in the implementation of L-norm minimal Neumann boundary controls for the wave equation. The optimal controls are computed as solutions of problems of exact optimal control, that is if they are implemented without delay, they steer the system to a position of rest in a given finite time T. We show that arbitrarily small delays δ > 0 can have a destabilizing effect in the sense that we can find initial states such that if the optimal control u is implemented in the form yx(t, 1) = u(t - δ) for t > δ, the energy of the system state at the terminal time T is almost twice as big as the initial energy. We also show that for more regular initial states, the effect of a delay in the implementation of the optimal control is bounded above in the sense that for initial positions with derivatives of BV -regularity and initial velocities with BV -regularity, the terminal energy is bounded above by the delay δ multiplied with a factor that depends on the BV-norm of the initial data. We show that for more general hyperbolic optimal exact control problems the situation is similar. For systems that have arbitrarily large eigenvalues, we can find terminal times T and arbitrarily small time delays δ, such that at the time T + δ, in the optimal control loop with delay the norm of the state is twice as large as the corresponding norm for the initial state. Moreover, if the initial state satisfies an additional regularity condition, there is an upper bound for the effect of time delay of the order of the delay with a constant that depends on the initial state only.},
author = {Leugering, Günter and Gugat, Martin},
doi = {10.1051/cocv/2015038},
faupublication = {yes},
journal = {Esaim-Control Optimisation and Calculus of Variations},
peerreviewed = {Yes},
title = {{Time} delay in optimal control loops for wave equations},
year = {2015}
}
@article{faucris.106688824,
author = {Rüffler, Fabian and Hante, Falk},
doi = {10.1016/j.nahs.2016.05.001},
faupublication = {yes},
journal = {Nonlinear Analysis: Hybrid Systems},
keywords = {Partial differential equation },
pages = {215 - 227},
peerreviewed = {unknown},
title = {{Optimal} switching for hybrid semilinear evolutions},
url = {http://www.sciencedirect.com/science/article/pii/S1751570X16300231},
volume = {22},
year = {2016}
}
@article{faucris.110509124,
abstract = {In many decision problems, criteria occur that can be expressed as ratios. The corresponding optimization problems are nonconvex programs of fractional type. In this paper, an algorithm for the numerical solution of these problems is introduced that converges always at superlinear speed. Numerical examples are presented.},
author = {Gugat, Martin},
doi = {10.1287/mnsc.42.10.1493},
faupublication = {no},
journal = {Management Science},
keywords = {Algorithm; Convex Auxiliary Problem; Decision Analysis; Dual Solutions; Generalized Fractional Programs; Multiple Criteria; Superlinear Convergence},
note = {UnivIS-Import:2015-03-05:Pub.1996.nat.dma.lama1.afasta},
pages = {1493-1499},
peerreviewed = {Yes},
title = {{A} {Fast} {Algorithm} for a {Class} of {Generalized} {Fractional} {Programs}},
volume = {42},
year = {1996}
}
@phdthesis{faucris.108545404,
author = {Jahn, Johannes},
faupublication = {no},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Sequentieller} {Innerer}-{Punkt}-{Algorithmus} zur {Lösung} nichtlinearer {Optimierungsprobleme}},
year = {1978}
}
@article{faucris.110515064,
abstract = {An algorithm for constrained rational Chebyshev approximation is introduced that combines the idea of an algorithm due to Hettich and Zencke, for which superlinear convergence is guaranteed, with the auxiliary problem used in the well-known original differential correction method. Superlinear convergence of the algorithm is proved. Numerical examples illustrate the fast convergence of the method and its advantages compared with the algorithm of Hettich and Zencke. © J.C. Baltzer AG Science Publishers.},
author = {Gugat, Martin},
doi = {10.1007/BF02143129},
faupublication = {no},
journal = {Numerical Algorithms},
keywords = {Newton's method; Parametric auxiliary problem; Parametric optimization; Rational Chebyshev approximation with constrained denominators; Superlinear convergence; 41A20; 65D15; 90C32; 90C34},
note = {UnivIS-Import:2015-03-05:Pub.1996.nat.dma.lama1.thenew},
pages = {107-122},
peerreviewed = {Yes},
title = {{The} {Newton} differential correction algorithm for rational {Chebyshev} approximation with constrained denominators},
url = {http://link.springer.com/article/10.1007/BF02143129},
volume = {13},
year = {1996}
}
@incollection{faucris.122683924,
abstract = {The purpose of this paper is to disduss, in a fairly heuristic way, certain aspects of modelling and controllability of flexible, multi-beam structures from the point of view of local modelling of the structure by distributed parameter systems.},
address = {Berlin, Heidelberg},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
booktitle = {System Modelling and Optimization - Proceedings of the 15th IFIP Conference Zurich, Switzerland, September 2–6, 1991},
doi = {10.1007/BFb0113314},
editor = {L.D. Davisson; A.G.J. MacFarlane; H. Kwakernaak; J.L. Massey; Ya Z. Tsypkin; A.J. Viterbi; Peter Kall},
faupublication = {no},
isbn = {978-3-540-47220-9},
month = {Jan},
pages = {467-480},
peerreviewed = {unknown},
publisher = {New York; Springer; 1999},
series = {Lecture Notes in Control and Information Sciences},
title = {{MODELING} {AND} {CONTROLLABILITY} {OF} {NETWORKS} {OF} {THIN} {BEAMS}},
url = {http://link.springer.com/chapter/10.1007/BFb0113314},
volume = {180},
year = {1992}
}
@article{faucris.112462504,
abstract = {For vibrating systems, a delay in the application of a feedback control may destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end.

We show that certain delays in the boundary feedback preserve the exponential stability of the system. In particular, we show that the system is exponentially stable with delays freely switching between the values 4Lc and 8Lc, where L is the length of the string and c is the wave speed. © 2011 Elsevier B.V. All rights reserved.}, author = {Gugat, Martin and Tucsnak, Marius}, doi = {10.1016/j.sysconle.2011.01.004}, faupublication = {yes}, journal = {Systems & Control Letters}, keywords = {Boundary feedback; Delay; Feedback stabilization of pdes; Feedback with delay; Hyperbolic pde; Past observation; String; Switching delay; Wave equation}, note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.anexam}, pages = {226-230}, peerreviewed = {Yes}, title = {{An} example for the switching delay feedback stabilization of an infinite dimensional system: {The} boundary stabilization of a string}, volume = {60}, year = {2011} } @article{faucris.122291224, abstract = {We consider a thin elastic plate with piezo patches mounted on top of it. Electrodes are located on the upper and, depending on the devices, at the lower surface of the patches. This piezo actuator is coupled to an elastic body. We develop an asymptotic procedure to derive a two-dimensional approximation of the entire structure. As a result, we obtain an inhomogeneous fourth-order plate equation with piecewise smooth coefficients for the vertical displacement coupled to a second-order in-plane problem. The analysis and the resulting asymptotic limits help clarifying the modeling issue concerning active piezo devices in multidimensional smart structures. Copyright © 2012 John Wiley & Sons, Ltd.}, author = {Leugering, Günter and Nazarov, Serguei A. and Slutskij, Andrey S.}, doi = {10.1002/mma.1566}, faupublication = {yes}, journal = {Mathematical Methods in the Applied Sciences}, keywords = {anisotropic material; Asymptotic analysis; effective material; piezoelectric material; plate equation}, pages = {633-658}, peerreviewed = {Yes}, title = {{Asymptotic} analysis of {3D} thin anisotropic plates with a piezoelectric patch}, volume = {35}, year = {2012} } @article{faucris.217146730, abstract = {A constructive method with modular structure is used to obtain the local exact boundary controllability for a coupled system of quasilinear wave equations with local or non-local dynamical boundary conditions. Some applications are given for the chain-like or star-like system of strings coupled via elastic springs, and of strings coupled via Maxwell-type and Kelvin-type viscoelastic springs, respectively.}, author = {Wang, Yue and Leugering, Günter and Li, Tatsien}, doi = {10.1016/j.nonrwa.2019.02.006}, faupublication = {yes}, journal = {Nonlinear Analysis-Real World Applications}, keywords = {Constructive method; Coupled system of quasilinear wave equations; Dynamical boundary condition; Exact boundary controllability; Hidden regularity}, note = {CRIS-Team Scopus Importer:2019-05-09}, pages = {71-89}, peerreviewed = {Yes}, title = {{Exact} boundary controllability and its applications for a coupled system of quasilinear wave equations with dynamical boundary conditions}, volume = {49}, year = {2019} } @article{faucris.121354464, author = {Gugat, Martin}, doi = {10.1137/080725921}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {wave equation, Tychonov regularization, PDE constrained optimization, penal- ization, exact penalty, exact controllability, state constraints, smoothed exact penalty, speed of convergence, hyperbolic PDE, optimal control}, note = {UnivIS-Import:2015-03-09:Pub.2009.nat.dma.zentr.penalt}, pages = {3026-3051}, peerreviewed = {Yes}, title = {{Penalty} {Techniques} for {State} {Constrained} {Optimal} {Control} {Problems} with the {Wave} {Equation}}, url = {http://epubs.siam.org/doi/abs/10.1137/080725921}, volume = {48}, year = {2009} } @article{faucris.117284244, abstract = {We present the topology optimization of an assembly consisting of a piezoelectric layer attached to a plate with support. The optimization domain is the piezoelectric layer. Using the SIMP (Solid Isotropic Material with Penalization) method with forced vibrations by harmonic electrical excitation, we achieve a maximization of the dynamic displacement. We show that the considered objective function can be used under certain boundary conditions to optimize the sound radiation. The vibrational patterns resulting from the optimization are analysed in comparison with the modes from an eigenvalue analysis. Multiple-frequency optimization is achieved by adaptive weighted sums. As a second optimization criterion, a flat frequency response is integrated in the optimization process. }, author = {Wein, Fabian and Kaltenbacher, Manfred and Leugering, Günter and Bänsch, Eberhard and Schury, Fabian}, doi = {10.3233/JAE-2009-1022}, faupublication = {yes}, journal = {International Journal of Applied Electromagnetics and Mechanics}, keywords = {Topology optimization; piezoelectric coupling; sound radiation}, month = {Jan}, pages = {201-221}, peerreviewed = {Yes}, title = {{Topology} optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation}, url = {http://content.iospress.com/articles/international-journal-of-applied-electromagnetics-and-mechanics/jae01022}, volume = {30}, year = {2009} } @incollection{faucris.121857384, address = {Stuttgart}, author = {Peukert, Wolfgang and Schwarzer, Hans-Christoph and Leugering, Günter}, booktitle = {Produktgestaltung in der Partikeltechnologie}, editor = {U. Teipel}, faupublication = {no}, isbn = {3-8167-6204-2}, keywords = {nano; particle; product;}, note = {UnivIS-Import:2015-04-20:Pub.2002.tech.ITC.mechve.guidel}, pages = {-}, peerreviewed = {No}, publisher = {Fraunhofer-IRB Verlag}, series = {Produktgestaltung in der Partikeltechnologie.}, title = {{Guidelines} for the production of nanoscaled particles and products}, year = {2002} } @article{faucris.214897680, abstract = {This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, from which the solutions along the beams can be reconstructed. Consequently analytic solutions for the network can be computed by a numerical scheme without applying a spacial discretization. While the assembly of the local stiffness matrices is slightly more expensive compared to an FE model using, e.g., linear ansatz-functions, the complexity of the solution of the FE-system is not. This is particularly interesting for topology and material optimization problems formulated on the network. In order to demonstrate the efficiency of the approach a numerical comparison to the case of linear ansatz-functions is provided followed by a series of studies with topology and multi-material optimization problems on networks.}, author = {Kufner, Tobias and Leugering, Günter and Semmler, Johannes and Stingl, Michael and Strohmeyer, Christoph}, doi = {10.1051/m2an/2018065}, faupublication = {yes}, journal = {Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique}, note = {CRIS-Team WoS Importer:2019-03-29}, pages = {2409-2431}, peerreviewed = {Yes}, title = {{SIMULATION} {AND} {STRUCTURAL} {OPTIMIZATION} {OF} {3D} {TIMOSHENKO} {BEAM} {NETWORKS} {BASED} {ON} {FULLY} {ANALYTIC} {NETWORK} {SOLUTIONS}}, volume = {52}, year = {2019} } @incollection{faucris.107386224, abstract = {A new method and algorithm for the efficient solution of a class of nonlinear semidefinite programming problems is introduced. The new method extends a concept proposed recently for the solution of convex semidefinite programs based on the sequential convex programming (SCP) idea. In the core of the method, a generally non-convex semidefinite program is replaced by a sequence of subproblems, in which nonlinear constraint and objective functions defined in matrix variables are approximated by block separable convex models. Global convergence is proved under reasonable assumptions. The article is concluded by numerical experiments with challenging Free Material Optimization problems subject to displacement constraints.}, author = {Stingl, Michael and Kocvara, Michal and Leugering, Günter}, booktitle = {Optimal control of coupled systems of partial differential equations}, doi = {10.1007/978-3-7643-8923-9_16}, faupublication = {yes}, pages = {275--295}, peerreviewed = {unknown}, series = {Internat. Ser. Numer. Math.}, title = {{A} {New} {Non}-linear {Semidefinite} {Programming} {Algorithm} with an {Application} to {Multidisciplinary} {Free} {Material} {Optimization}}, volume = {158}, year = {2009} } @article{faucris.120013784, abstract = {We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.}, author = {Gugat, Martin and Leugering, Günter and Martin, Alexander and Schmidt, Martin and Sirvent, Mathias and Wintergerst, David}, doi = {10.1007/s10589-017-9970-1}, faupublication = {yes}, journal = {Computational Optimization and Applications}, keywords = {Mixed-integer optimal control, Instantaneous control, Partial differential equations on graphs, Gas networks, Mixed-integer linear optimization.}, pages = {267-294}, peerreviewed = {Yes}, title = {{MIP}-based instantaneous control of mixed-integer {PDE}-constrained gas transport problems}, volume = {70}, year = {2018} } @inproceedings{faucris.117915204, abstract = {The authors introduce nonlinear equations describing the vibrations in space of networks of elastic strings and beams. Linearization about an equilibrium configuration yields a hyperbolic system of linear equations coupled by conditions at the multiple nodes where several network members meet. The authors study the controllability of these systems by controls exercised at some nodes. The multiplier method yields a priori inequalities guaranteeing exact controllability, and hence stabilizability, for certain rudimentary networks.}, author = {Leugering, Günter and Schmidt, E. J. P. Georg}, booktitle = {Decision and Control, 1989., Proceedings of the 28th IEEE Conference}, date = {1989-12-13/1989-12-15}, doi = {10.1109/CDC.1989.70580}, editor = {IEEE}, faupublication = {no}, keywords = {Nonlinear equations; Potential energy; Mathematics; Controllability; Control systems; Mathematical model; Kinetic energy; Partial differential equations; Statistics; Councils}, month = {Jan}, pages = {2287-2290}, peerreviewed = {unknown}, publisher = {IEEE Xplore}, title = {{ON} {THE} {CONTROL} {OF} {NETWORKS} {OF} {VIBRATING} {STRINGS} {AND} {BEAMS}}, url = {http://ieeexplore.ieee.org/document/70580/}, year = {1989} } @inproceedings{faucris.106458924, author = {Rathmann, Wigand}, booktitle = {1. Tag der Lehre}, date = {2015-12-11}, faupublication = {yes}, peerreviewed = {No}, title = {{Mathematische} {Fragestellungen} online realisieren ({Vortrag} beim 1. {Tag} der {Lehre} an der {FAU})}, url = {https://youtu.be/GEvyM2vhm_E?iframe=true}, venue = {FAU}, year = {2015} } @inproceedings{faucris.120849784, abstract = {We consider a system of 1-d-diffusion-convection equations on graphs as being representative of flow or transport problems in channel, pipeline or root-systems appearing in many applications. Such systems are subject to controls the effect of which one wants to optimize. In these notes we discuss the mathematical framework of typical optimal control problems of such systems on graphs. We focus on singular perturbations with respect to diffusion and on the numerical implementation.}, author = {Leugering, Günter and Fischer, Thorsten}, faupublication = {yes}, month = {Jan}, pages = {69-97}, peerreviewed = {unknown}, title = {{On} instantaneous control of singularly perturbed hyperbolic equations on graphs}, volume = {219}, year = {2001} } @inproceedings{faucris.200190269, author = {Rathmann, Wigand and Hild, Johannes}, booktitle = {Proceedings 14. Workshop Mathematik in ingenieurwissenschaftlichen Studiengängen}, date = {2017-09-18/2017-09-18}, editor = {Gottlob-Frege-Zentrum, Hochschule Wismar}, faupublication = {yes}, isbn = {978-3-942100-55-7}, peerreviewed = {unknown}, title = {{Optimale} {Steuerung} von {Flachwasserkanälen}}, venue = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, year = {2017} } @article{faucris.219579007, author = {Ray, Nadja and Oberlander, Jens and Frolkovic, Peter}, faupublication = {yes}, journal = {Computational Geosciences}, peerreviewed = {Yes}, title = {{Numerical} investigation of a fully coupled micro-macro model for mineral dissolution and precipitation}, year = {2019} } @article{faucris.123264724, abstract = {We consider hot forming processes, in which a metal solid body is deformed by several rolls in order to obtain a desired final shape. To minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible, we formulate an optimal control problem where we use the trajectories of the rolls as control functions. The deformation of the solid body is described through the basic equations of nonlinear continuum mechanics, which are here coupled with an elasto-viscoplastic material model based on a multiplicative split of the deformation gradient. We assume that the deformations of the rolls can be neglected, thus we add unilateral frictional contact boundary conditions, resulting in an evolutionary quasi-variational inclusion. The associated control-to-observation map is non-differentiable due to changes of state between elastic and plastic material behavior, contact and separation and stick and slip motion, yet we still want to apply gradient-based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist. To resolve this issue, we first regularize all non-differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information. Finally, we formulate a suitable algorithm and discuss numerical results for a real-world example to illustrate its capability. (C) 2017 Elsevier B.V. All rights reserved.}, author = {Werner, Stefan and Stingl, Michael and Leugering, Günter}, doi = {10.1016/j.cma.2017.03.006}, faupublication = {yes}, journal = {Computer Methods in Applied Mechanics and Engineering}, keywords = {Optimal control; Regularization; Sensitivity analysis; Nonlinear continuum mechanics; Frictional contact; Elasto-viscoplasticity}, pages = {442-471}, peerreviewed = {Yes}, title = {{Model}-based control of dynamic frictional contact problems using the example of hot rolling}, volume = {319}, year = {2017} } @article{faucris.119326284, abstract = {

In this paper, a new Ansatz for modelling the Baculovirus infection cycle is presented. The base of this model is the cell cycle distribution at the time of infection. It is possible to calculate the growth of the culture and the initiation of virus processing by considering cell cycle distribution. By taking into account the length of the viral genome and the polymerase activity, it is possible to calculate the virus production rate, which underlies a logistic growth. In the present work, a new hypothesis explaining the accelerated death rates of infected cells has been introduced. This assumption provides the possibilities of performing calculation without any fixed time intervals. The simulation was tested by comparing experimental data with the model prediction. Therefore, cell cycle distributions over the culture time and the growth behaviour of infected and non-infected insect cells were measured. A model, Baculovirus coding for GFP was employed for the present investigation, as it allows tracking the infection and determining the effectiveness of the infection, which is highly dependent on the cell density at the time of infection (TOI). Furthermore, the new model is is taken to simulate data gained from literature about virus release and adsorption. The new assumptions make the model more independent to fit into different cultivation systems.

}, author = {Lindenberger, Christoph and Pflug, Lukas and Hübner, Holger and Buchholz, Rainer}, doi = {10.1007/s12257-011-0371-5}, faupublication = {yes}, journal = {Biotechnology and Bioprocess Engineering}, keywords = {baculovirus; modelling; insect cells; infection cycle}, pages = {211-217}, peerreviewed = {Yes}, title = {{A} novel model for studying baculovirus infection process}, url = {http://link.springer.com/article/10.1007/s12257-011-0371-5}, volume = {17}, year = {2012} } @article{faucris.120457084, author = {Jahn, Johannes and Luc, D.T.}, faupublication = {yes}, journal = {Numerical Functional Analysis and Optimization}, note = {UnivIS-Import:2015-03-05:Pub.1992.nat.dma.pama21.axioma}, pages = {305-326}, peerreviewed = {Yes}, title = {{Axiomatic} {Approach} to {Duality} in {Optimization}}, volume = {13}, year = {1992} } @article{faucris.110282524, abstract = {In this paper an interior point method is presented for nonlinear programming problems with inequality constraints. On defining a modified distance function the original problem is solved sequentially by using a method of feasible directions. At each iteration a usable feasible direction can be determined explicitly. Under certain assumptions it can be shown that every accumulation point of the sequence of points constructed by the proposed algorithm satisfies the Kuhn-Tucker conditions. © 1979 Physica-Verlag.}, author = {Jahn, Johannes}, doi = {10.1007/BF01917332}, faupublication = {no}, journal = {Mathematical Methods of Operations Research}, note = {UnivIS-Import:2015-03-05:Pub.1979.nat.dma.pama21.aninte}, pages = {1-15}, peerreviewed = {Yes}, title = {{An} {Interior} {Point} {Method} for {Nonlinear} {Programming}}, volume = {23}, year = {1979} } @article{faucris.123311144, abstract = {We analyze the subcritical gas flow through fan-shaped networks of pipes, that is, through tree-shaped networks with exactly one node where more than two pipes meet. The gas flow in pipe networks is modeled by the isothermal Euler equations, a hyperbolic PDE system of balance laws. For this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval. Furthermore, we present a Lyapunov function and boundary feedback laws to stabilize a fan-shaped network around a given stationary state. © 2011 Society for Industrial and Applied Mathematics.}, author = {Gugat, Martin and Hirsch-Dick, Markus and Leugering, Günter}, doi = {10.1137/100799824}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {Classical solutions; Critical length; Fan-shaped networks; Feedback law; Gas networks; Junction; Lyapunov function; Networked hyperbolic systems; Riemann invariants}, note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.gasflo}, pages = {2101-2117}, peerreviewed = {Yes}, title = {{Gas} {Flow} in {Fan}-{Shaped} {Networks}: {Classical} {Solutions} and {Feedback} {Stabilization}}, url = {http://epubs.siam.org/sicon/resource/1/sjcodc/v49/i5/p2101_s1}, volume = {49}, year = {2011} } @article{faucris.119866164, author = {Jahn, Johannes}, faupublication = {yes}, journal = {Journal of Multi-Criteria Decision Analysis}, note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.pama21.onthed}, pages = {17-24}, peerreviewed = {Yes}, title = {{On} the {Determination} of {Minimal} {Facets} and {Edges} of a {Polyhedral} {Set}}, volume = {6}, year = {1997} } @article{faucris.122946824, abstract = {We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the