On the Optimal Control Problem for Bilinear Systems with Bounded and Unbounded Controls

Abstract

In the present chapter, we address the problem of optimal control of bilinear systems with unbounded and bounded controls. The main purpose of this study is to establish the existence of an optimal control, which is characterized by a solution of an optimality system. Additionally, we provide a sufficient condition for the uniqueness of such a control. The results obtained are applied to various specific control sets. Furthermore, we present a numerical algorithm for computing the optimal control and successfully demonstrate its application through simulations involving heat equations.