Regional quadratic control problem for distributed bilinear systems with bounded controls

摘要

The aim of this paper is to study regional quadratic control problem for a distributed bilinear system evolving in a spatial domain Ω. The question is to obtain a bounded feedback control that drives such a system from an initial state to a desired one in finite time, only on a subregion ω of Ω, and minimises a quadratic functional cost. Our purpose is to prove that an optimal control exists, and characterised as solution of an optimality system. The approach is successfully illustrated by simulations.