Regional gradient optimal control problem governed by a distributed bilinear systems

Abstract

This paper gives an extension of previous work on gradient optimal control of distributed parabolic systems to the case of distributed bilinear systems which are a type of nonlinear systems. We introduce the notion of flux optimal control of distributed bilinear systems. The idea is trying to achieve a neighborhood of the gradient state of the considered system by minimizing a nonlinear quadratic cost. Using optimization techniques, a method showing how to reach a desired flux at a final time, only on internal subregion of the system domain will be proposed. The proposed simulation illustrates the theoretical approach by commanding the heat bilinear equation flux to a desired profile.

Regional averaged control problems with minimum energy constrained by distributed parabolic systems

“…Following this, there are several works dedicatory to the control and analysis of the parabolic distributed systems, for examples, [2][3][4]. In the last decades, several researches have been devoted to the study of the problem of regional controllability [8] and also of the gradient controllability [7,9,10].…”