Dimensional Optimal Control Problem Research Articles

On parametric evolution inclusions of the subdifferential type with applications to optimal control problems

In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusion. Then we study how these results can be used to examine the sensitivity properties (variational stability) of certain broad classes of nonlinear infinite dimensional optimal control problems. Some examples are worked out in detail, illustrating the applicability of our work. These include obstacle problems (with time varying obstacles), optimal control of distributed parameter systems, and differential variational inequalities.

Variational stability of infinite dimensional optimal control problems

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.