Regional Controllability of Semi-Linear Distributed Parabolic Systems: Theory and Simulation

Abstract

The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achieving internal and boundary regional controllability. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) and Schauder's fixed point theorem. We give a numerical example developed in internal and boundary sub region. These numerical illustrations show the efficiency of the approach and lead to conjectures.

Regional Quadratic Problem for Distributed Bilinear Systems With Bounded Controls

“…Let u n (x, t) = u Qn (x, t), we conclude from (8), that ||u n || W are uniformly bounded independently of n.…”

Gradient Controllability for Hyperbolic Systems

“…The problem where the subregion target is a part of the boundary of the system evolution domain, is of great interest and the work is under consideration and will be the subject of the feature paper. We are also interested to control the gradient of semilinear systems which are very close to nonlinear ones, and then we try to extend the existed results given in observability (see [8]and [9]) and controllability (see [10]) of semilinear systems to gradient case.…”

Regional gradient optimal control problem governed by a distributed bilinear systems

“…The gradient optimal control concerns the optimal control of the gradient state to a subregion of the system domain. The readers can obtain very interest contributions in this field, particularly characterizations of the optimal control that achieves regional gradient controllability by Zerrik et all in [9] and Kamal et al [10] in the case of parabolic linear systems, and Ould Beinane et all [11] in the case of semi linear systems.…”