ON THE OPTIMAL-CONTROL AND RELAXATION OF FINITE DIMENSIONAL SYSTEMS DRIVEN BY MAXIMAL MONOTONE DIFFERENTIAL-INCLUSIONS

In this paper we examine finite dimensional optimal control problems driven by maximal monotone differential inclusions and having state dependent control constraints. First, with the help of a convexity hypothesis, we prove the existence of optimal admissible pairs. Then we drop convexity hypothesis and we look at the relaxed system. For that system we establish the existence of optimal solutions under minimal hypotheses. Finally, by strengthening our hypotheses we show that the original trajectories are dense in the relaxed ones for the topology of uniform convergence and that the two problems relaxed and original have the same value.