Constrained regional control problem for distributed bilinear systems

In this study, the authors consider the problem of optimal regional controllability of a distributed bilinear system evolving in a spatial domain Ω. The question is to obtain a bounded feedback control with minimum energy that drives such a system from an initial state to a desired one in finite time, only on a subregion ω of Ω. The purpose of this study is to prove that a regional optimal control exists, and characterised as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.