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Control of the Wave Equation by Time-Dependent Coefficient

Antonin Chambolle, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 the rich behavior of...

Control of transonic shock positions

Olivier Pironneau (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Control of Transonic Shock Positions

Olivier Pironneau (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Control of Traveling Solutions in a Loop-Reactor

Y. Smagina, M. Sheintuch (2010)

Mathematical Modelling of Natural Phenomena

We consider the stabilization of a rotating temperature pulse traveling in a continuous asymptotic model of many connected chemical reactors organized in a loop with continuously switching the feed point synchronously with the motion of the pulse solution. We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is updated at every step on-line using the discrepancy between the temperature at the front...

Control of underwater vehicles in inviscid fluids

Rodrigo Lecaros, Lionel Rosier (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local controllability...

Control problems for convection-diffusion equations with control localized on manifolds

Phuong Anh Nguyen, Jean-Pierre Raymond (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain optimality...

Control problems for convection-diffusion equations with control localized on manifolds

Phuong Anh Nguyen, Jean-Pierre Raymond (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain...

Contrôle et stabilisation d'ondes électromagnétiques

Kim Dang Phung (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.

Contrôle par les coefficients dans le modèle Elrod-Adams

Mohamed El Alaoui Talibi, Abdellah El Kacimi (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Dans ce papier, nous étudions un problème de contrôle par les coefficients issu de la lubrification élastohydrodynamique. La variable de contrôle est l’épaisseur du fluide. Le phénomène de cavitation est pris en compte par le modèle Elrod-Adams, connu pour ses performances dans la conservation des débits d’entrée et de sortie. L’idée est de régulariser dans l’équation d’état le graphe d’Heaviside, en l’approchant par une suite de fonctions monotones et régulières. Nous dérivons les conditions d’optimalité...

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