Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space (Q1066080)

Using Cesari's approach, we prove the existence of optimal controls for a class of systems governed by differential inclusions on a Banach space having the Radon-Nikodym property. The existence theorem for optimal relaxed controls under fairly general assumptions on the system and the admissible controls is given. This result depends on a fundamental result, that proves the existence of mild solutions of differential inclusions on a Banach space, which has also independent interest. Further preparatory lemmas, are also useful in the study of time-optimal and terminal control problems. For illustration of the results, we present two examples, one on distributed controls for a class of systems governed by nonlinear parabolic equations and the other on boundary controls with discontinuous boundary operator.