Martin Gugat

L p -Optimal Boundary Control for the Wave Equation

We study problems of boundary controllability with minimal Lp--norm (

Modelling, Stabilization, and Control of Flow in Networks of Open Channels

p\in [2,\infty]

Analytic solutions of L∞ optimal control problems for the wave equation

) for the one-dimensional wave equation, where the state is controlled at both boundaries through Dirichlet or Neumann conditions. The problem is to reach a given terminal state and velocity in a given finite time, while minimizing the Lp--norm of the controls. We give necessary and sufficient conditions for the solvability of this problem. We show as follows how this infinite-dimensional optimization problem can be transformed into a problem which is much simpler: The feasible set of the transformed problem is described by a finite number of simple pointwise equality constraints for the control function in the Dirichlet case while, in the Neumann case, an additional integral equality constraint appears. We provide explicit complete solutions of the problems for all

Regularization of L ∞ -Optimal Control Problems for Distributed Parameter Systems

p\in[2,\infty]

Exponential Stabilization of the Wave Equation by Dirichlet Integral Feedback

in the Dirichlet case and solutions for some typical examples in the Neumann case.

Classical solutions and feedback stabilization for the gas flow in a sequence of pipes

In this paper we present a model for the controlled flow of a fluid through a network of channels using a coupled System of St Venant equations. We generalize in a variety of ways recent results of Coron, d’Andrea-Novel and Bastin concerning the stabilizability around equilibrium of the flow through a single channel to serially connected channels and finally to networks of channels. The work presented here is entirely based on the theory of quasilinear hyperbolic Systems. We also consider open-loop optimal control problems and provide numerical schemes both for the simulation and the control of such Systems.

Global controllability between steady supercritical flows in channel networks

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.

L ∞ -NORM MINIMAL CONTROL OF THE WAVE EQUATION: ON THE WEAKNESS OF THE BANG-BANG PRINCIPLE

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.

Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction

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

Optimal distributed control of the wave equation subject to state constraints

L^2