Optimal control problems for a class of non-linear evolution equations

Abstract

In this paper we consider optimal control problems for infinite-dimensional systems governed by non-linear evolution equations. We show that the set of trajectories of such systems is compact in a space of continuous functions, and then using this fact we solve Lagrange and time optimal control problems. Then we concentrate on linear systems and we prove a new ‘bang-bang’ principle and a corresponding maximum principle. We conclude with an example of a control system governed by a non-linear parabolic partial differential equation.