Regional optimal control problem of a class of infinite-dimensional bi-linear systems

The purpose of this paper is to study regional optimal control of an infinite-dimensional bi-linear system, excited by unbounded or bounded controls. Then we prove the existence of an optimal control that minimises a functional cost and we give the characterisation of such a control. Also we give the condition that ensures the uniqueness of the optimal control. The obtained results lead to an algorithm that we illustrate by simulations for a bi-dimensional diffusion system excited by a zone actuator.