Existence of optimal controls for a class of nonlinear distributed parameter systems

Abstract

In this paper we examine a Lagrange optimal control problem driven by a nonlinear evolution equation involving a nonmonotone, state dependent perturbation term. For this problem we establish the existence of optimal admissible pairs. For the same system we also examine a time optimal control problem involving a moving target set. Finally we work out in detail an example of a strongly nonlinear parabolic distributed parameter system.