Bounded and unbounded optimal control for infinite dimensional bilinear systems

Abstract

In this paper, we consider optimal control of infinite dimensional bilinear systems in both cases unbounded and bounded controls set. Then, we minimise a functional cost constituted of the deviation between the desired state and the final one at time T, the effort term and the energy one. The purpose of this study is to prove that an optimal control exists and characterised as a solution to an optimality system. Thus we give a sufficient condition for the uniqueness of such a control. The obtained results are applied to many particular controls sets. Numerical algorithm for the computation of an optimal control is given and successfully illustrated through simulations for the heat and transport equations.

Keywords:

• Bilinear systems
• controllability
• optimal control
• $C_0$-semigroups

Disclosure statement

No potential conflict of interest was reported by the authors.