Variational stability of infinite dimensional optimal control problems

Abstract

We examine the variational stability of infinite dimensional optimal control problems governed by non-linear evolution equations. Our tools are the Kuratowski-Mosco convergence of sets and the corresponding τ-convergence of functions. We prove the τ-convergence of cost functionals, the convergence of the values of the problems and we examine the variational stability of the solution and reachable sets. These results are then applied to a sequence of non-linear parabolic distributed parameter optimal control problems.