DIFFERENTIAL INCLUSIONS ON BANACH SPACES AND THEIR OPTIMAL CONTROL

Abstract

In this paper we consider a class of control systems governed by Differential inclusions on Banach spaces. For any fixed control policy, we prove the existence of a nonempty set of solutions for the system. Using this we then prove the existence of optimal controls for certain control problems. The paper is concluded with some results on relaxed controls and some comments on open problems in the area.