On the dependence of the solutions and optimal solutions of control problems on the control constraint set

AbstractIn this paper we examine the dependence of the solutions and optimal solutions of a class of linear, infinite-dimensional control systems on the control constraint set. This is done using the weak and the Kuratowski-Mosco convergence of sets. First we establish some general facts about weakly convergent multifunctions. Then we prove some convergence theorems for the trajectories of certain control systems. We also derive a general relaxation theorem. Subsequently we pass to optimal control problems and prove various convergence results. We conclude with an example from parabolic control systems