A CLASS OF SEMILINEAR INFINITE DIMENSIONAL UNCERTAIN SYSTEMS ON BANACH SPACES CONTROLLED BY VECTOR MEASURES CONTAINING DIRAC MEASURES

Abstract

In this paper we consider a class of semilinear uncertain dynamic systems on Banach spaces subject to dynamic and additive uncertainty without any probabilistic structure. The problem is to find a control law that minimizes the maximum risk. We present two distinct results on the existence of optimal controls in the presence of system uncertainty and additive unstructured disturbance. The first result is concerned with the question of existence of optimal controls from the class of general vector measures, and the second result is concerned with the question of existence of optimal policies from the class of purely impulsive controls.