Caractérisation d'un espace fonctionnel intervenant en contrôle optimal
Characterization of optimal shapes and masses through Monge-Kantorovich equation
We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.
Chebyshev semi-iteration in preconditioning for problems including the mass matrix.
Comportements limites des solutions de certains problèmes mixtes pour des équations paraboliques et leurs applications
Computing optimal control with a quasilinear parabolic partial differential equation.
Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût
Conical differentiability for bone remodeling contact rod models
We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement...
Conical differentiability for bone remodeling contact rod models
We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement constraint...
Conservation law constrained optimization based upon front-tracking
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...
Conservation law constrained optimization based upon Front-Tracking
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...
Contact problems with given time-dependent friction force in linear viscoelasticity
Control for hyperbolic equations
Control for the Sine-Gordon equation
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Control for the sine-gordon equation
In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Control of a system governed by Dirichlet problem
Control of the surface of a fluid by a wavemaker
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Control of the surface of a fluid by a wavemaker
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in Lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Control of the wave equation by time-dependent coefficient
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...
Control of the Wave Equation by Time-Dependent Coefficient
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 problems for convection-diffusion equations with control localized on manifolds
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...