Regional optimal control of a bilinear plate equation

摘要

The aim of this paper is to study regional optimal control of a vibrating plate described by a bilinear systems evolving on a spacial domain Ω ⊂ ℝ². The question is meant to obtain a distributed control which minimizes a functional cost constituted of the deviation between a desired state and the reached one only on a subregion ω of Ω and the energy term. Hence, we prove that a minimizing control exists, and we give a characterization of optimal control. Also, algorithm is given and successfully illustrated by simulations.