On a Stability Theorem of the Optimal Control Problem For Quasi Optic Equation

In this paper, the finite difference method is applied to the optimal control problem of system governed by stationary equation of Quasi-Optic . For this aim, the finite difference scheme is constituted for considered optimal control problem. Obtained an estimation for the solution of this difference scheme, the error of the difference scheme is evaluated. Finally, the convergence according to the functional of the finite difference approximations is proved

Constructive solution of a bilinear optimal control problem for a Schrödinger equation

International audienceOften considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient constructive method for solving a certain class of optimal control problems. This paper aims both at extending the results already available about these algorithms in the finite dimensional case (i.e., the time-discretized case) and at completing those of the continuous case. This paper starts with some results about the regularity of a functional related to a wide class of model in quantum chemistry. Those enable us to extend an inequality due t