Displaying similar documents to “Control of the wave equation by time-dependent coefficient”

Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito, Karl Kunisch (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

Control of the Wave Equation by Time-Dependent Coefficient

Antonin Chambolle, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate...

Some applications of optimal control theory of distributed systems

Alfredo Bermudez (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we present some applications of the J.-L. Lions’ optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control

-Norm minimal control of the wave equation: on the weakness of the bang-bang principle

Martin Gugat, Gunter Leugering (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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For optimal control problems with ordinary differential equations where the L -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...