Fractional Optimal Control Problem of Parabolic Bilinear Systems with Bounded Controls

Abstract

The purpose of this paper is to study a fractional distributed optimal control for a class of infinite-dimensional parabolic bilinear systems evolving on a spatial domain Ω by distributed controls depending on the control operator. Using the Fréchet differentiability, we prove the existence of an optimal control depending on both time and space, that minimizes a quadratic functional which leads into account, the deviation between the desired state and the reached one. Then, we show characterizations of an optimal distributed control for different admissible controls set. Moreover, we developed an algorithm and give simulations that successfully illustrate the theoretically obtained results.