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.

shWwWe present the analysis for finding optimal locations and rotations of anisotropic material inclusions in a matrix material by using the polarization matrix. We compare different types of cost functionals, in particular local ones, and show their respective differences. We use the Eshelby theorem and the representation of stresses based on the link matrix. As an analytical model reduction technique, this allows for efficent numerical computation which is demonstrated for two selected examples.
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:utt + Δ2u = 0 (whereΔ2u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:uv = 0 and(Δu)v = ϕ = control. Thus, the state is the pair [u, ut] and controllability means existence ofϕ on Σ:= (0,T∂Ω transfering ‘any’[u, ut]0 to ‘any’[u, ut]T. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For largeT one has such controllability with∥ϕ∥ = O(T−1/2). More surprising is that (based on a harmonic analysis estimate ) one has controllability for arbitrarily short times (in contrast to the wave equation:utt = Δu) with log∥ϕ∥ = O(T−1) asT→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 , 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 C1-functions, so no shocks occur. Copyright © 2004 John Wiley & Sons, Ltd.}, author = {Gugat, Martin and Leugering, Günter and Schmidt, E. J. P. Georg}, doi = {10.1002/mma.471}, faupublication = {yes}, journal = {Mathematical Methods in the Applied Sciences}, keywords = {Global controllability; Network; Node conditions; St. Venant equations; Supercritical states}, note = {UnivIS-Import:2015-03-09:Pub.2004.nat.dma.zentr.global}, pages = {781-802}, peerreviewed = {Yes}, title = {{Global} controllability between steady supercritical flows in channel networks}, url = {http://www3.interscience.wiley.com/cgi-bin/abstract/108561139/ABSTRACT?CRETRY=1&SRETRY=0}, volume = {27}, year = {2004} } @article{faucris.117909924, abstract = {This paper is concerned with boundary control of one-dimensional vibrating media whose motion is governed by a wave equation with a 2n-order spatial self-adjoint and positive-definite linear differential operator with respect to 2n boundary conditions. Control is applied to one of the boundary conditions and the control function is allowed to vary in the Sobolev space W , p for p∈[2, ∞] With the aid of Banach space theory of trigonometric moment problems, necessary and sufficient conditions for null-controllability are derived and applied to vibrating strings and Euler beams.

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 L2-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.

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.

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.

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.

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.

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)

An integrodifferential equation of the Volterra type is considered under the action of anL2(0, T, L2(Γ))-boundary control. By harmonic analysis arguments it is shown that the controllability results obtained in  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.

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.
The 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.

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.