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} } @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} } @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} } @article{faucris.121019404, abstract = {The problem to control a finite string to the zero state in finite time from a given initial state by controlling the state at the two boundary points in such a way that the controls generate a continuous state is considered. The corresponding optimal control problem where the objective function is the LIn 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.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} } @article{faucris.109719104, abstract = {We consider traffic flow governed by the LWR model. We show that a Lipschitz continuous initial density with free-flow and sufficiently small Lipschitz constant can be controlled exactly to an arbitrary constant free-flow density in finite time by a piecewise linear boundary control function that controls the density at the inflow boundary if the outflow boundary is absorbing. Moreover, this can be done in such a way that the generated state is Lipschitz continuous. Since the target states need not be close to the initial state, our result is a global exact controllability result. The Lipschitz constant of the generated state can be made arbitrarily small if the Lipschitz constant of the initial density is sufficiently small and the control time is sufficiently long. This is motivated by the idea that finite or even small Lipschitz constants are desirable in traffic flow since they might help to decrease the speed variation and lead to safer traffic.}, author = {Gugat, Martin}, doi = {10.1155/2016/2743251}, faupublication = {yes}, journal = {Mathematical Problems in Engineering}, keywords = {Exact Controllability; Traffic Flow; Lipschitz Continuous; LWR model}, pages = {11}, peerreviewed = {Yes}, title = {{Exact} {Boundary} {Controllability} for {Free} {Traffic} {Flow} with {Lipschitz} {Continuous} {State}}, url = {http://www.hindawi.com/journals/mpe/2016/2743251/}, volume = {2016}, year = {2016} } @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} } @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 L
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.118068104, author = {Gugat, Martin and Wintergerst, David and Schultz, Rüdiger}, doi = {10.1007/s40314-016-0383-z}, faupublication = {yes}, journal = {Computational and Applied Mathematics}, keywords = {Stationary statesIsothermal Euler equationsz-FactorCompressibility factorReal gasNetworkNode conditionsGas transportGas network}, peerreviewed = {Yes}, title = {{Networks} of pipelines for gas with nonconstant compressibility factor: stationary states}, url = {http://link.springer.com/article/10.1007/s40314-016-0383-z}, year = {2016} } @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.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} } @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

`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.`

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.117458704, abstract = {We consider the isothermal Euler equations without friction that simulate gas flow through a pipe. We consider the problem of boundary stabilisation of this system locally around a given stationary state. We present a feedback law that is linear in the physical variables and yields exponential decay of the system state. For the numerical solution of hyperbolic systems of conservation laws, the Jin-Xin relaxation scheme can be used. Therefore, we also consider the boundary stabilisation of the relaxation system by the linear Riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system. © 2012 Taylor & Francis Group, LLC.}, author = {Hirsch-Dick, Markus and Gugat, Martin and Herty, Michael and Steffensen, Sonja}, doi = {10.1080/00207179.2012.703787}, faupublication = {yes}, journal = {International Journal of Control}, keywords = {boundary feedback stabilisation; conservation laws; isothermal Euler equations; Lyapunov function; relaxation scheme}, note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.zentr.onther}, pages = {1766-1778}, peerreviewed = {Yes}, title = {{On} the relaxation approximation of boundary control of the isothermal {Euler} equations}, volume = {85}, year = {2012} } @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}
}
@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.112463164,
abstract = {We study the isothermal Euler equations with friction and consider non-stationary solutions locally around a stationary subcritical state on a finite time interval. The considered control system is a quasilinear hyperbolic system with a source term. For the corresponding initial-boundary value problem we prove the existence of a continuously differentiable solution and present a method of boundary feedback stabilization. We introduce a Lyapunov function which is a weighted and squared H^{1}-norm of the difference between the nonstationary and the stationary state. We develop boundary feedback conditions which guarantee that the Lyapunov function and the H^{1}-norm of the difference between the non-stationary and the stationary state decay exponentially with time. This allows us also to prove exponential estimates for the C^{0}- and C^{1}- norm.},
author = {Hirsch-Dick, Markus and Gugat, Martin and Leugering, Günter},
doi = {10.3934/naco.2011.1.225},
faupublication = {yes},
journal = {Numerical Algebra, Control and Optimization},
keywords = {Boundary control; C; C; Conservation law; Distributed parameter system; Exponential stability; Feedback law; Feedback stabilization; Friction term; Gas network; H; Isothermal Euler equations; Lyapunov function; Riemann invariants},
note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.astric},
pages = {225-244},
peerreviewed = {Yes},
title = {{A} strict {H1}-{Lyapunov} function and feedback stabilization for the isothermal {Euler} equations with friction},
url = {http://www.aimsciences.org/journals/displayReferences.jsp?paperID=6330},
volume = {1},
year = {2011}
}
@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 *L* ^{2}-norm minimal control in terms of the given initial state. We show that if the initial state is sufficiently regular, the same control is also *L* ^{ p }-norm minimal for *p* > 2.},
author = {Gugat, Martin},
doi = {10.1007/s40065-014-0110-9},
faupublication = {yes},
journal = {Arabian Journal of Mathematics},
keywords = {35L05; 49J20; 93C20},
note = {UnivIS-Import:2015-03-09:Pub.2014.nat.dma.zentr.normmi},
pages = {41-58},
peerreviewed = {unknown},
title = {{Norm}-minimal {Neumann} boundary control of the wave equation},
url = {http://link.springer.com/article/10.1007/s40065-014-0110-9},
volume = {4},
year = {2014}
}
@article{faucris.117348704,
abstract = {We consider a network of pipelines where the flow is controlled by a number of compressors. The consumer demand is described by desired boundary traces of the system state. We present conditions that guarantee the existence of compressor controls such that after a certain finite time the state at the consumer nodes is equal to the prescribed data. We consider this problem in the framework of continuously differentiable states. We give an explicit construction of the control functions for the control of compressor stations in gas distribution networks. Copyright © 2010 John Wiley & Sons, Ltd.},
author = {Gugat, Martin and Herty, Michael and Schleper, Veronika},
doi = {10.1002/mma.1394},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
keywords = {exact controllability;nodal control of networked hyperbolic systems;nodal profile control;classical solutions},
note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.flowco},
pages = {745-757},
peerreviewed = {Yes},
title = {{Flow} control in gas networks: {Exact} controllability to a given demand},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1394/abstract},
volume = {34},
year = {2010}
}
@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.119915444,
abstract = {Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd denominator or vice versa.},
author = {Gugat, Martin},
doi = {10.1051/cocv:2001113},
faupublication = {no},
journal = {Esaim-Control Optimisation and Calculus of Variations},
keywords = {Eigenvalues; Exact controllability; Moment problem; Rotating Timoshenko beam; 93C20; 93B05; 93B60},
note = {UnivIS-Import:2015-03-09:Pub.2001.nat.dma.lama1.contro},
pages = {333-360},
peerreviewed = {Yes},
title = {{Controllability} of a slowly rotating {Timoshenko} beam},
url = {http://www.esaim-cocv.org/articles/cocv/abs/2001/01/cocvVol6-13/cocvVol6-13.html},
volume = {6},
year = {2001}
}
@misc{faucris.119422204,
abstract = {

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.110513084,
abstract = {The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.},
author = {Gugat, Martin},
doi = {10.1007/s003659900010},
faupublication = {no},
journal = {Constructive Approximation},
keywords = {41A20; 65D15; 90C32; 90C34; Chebyshev approximation; Constrained denominators; Differential correction algorithm; Fractional programming; Rational approximation},
note = {UnivIS-Import:2015-03-05:Pub.1996.nat.dma.lama1.analgo},
pages = {197-221},
peerreviewed = {Yes},
title = {{An} {Algorithm} for {Chebyshev} {Approximation} by {Rationals} with {Constrained} {Denominators}},
volume = {12},
year = {1996}
}
@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,