Sensitivity Properties of Parametric Nonconvex Evolution Inclusions with Application to Optimal Control Problems

The main concern of this paper is to investigate sensitivity properties of parametric evolution systems of first order involving a general class of nonconvex functions. Using recent results on the stability of the subdifferentials, with respect to the Gamma convergence, of the associated sequence of subsmooth or semiconvex functions, we give some continuity properties of the solution set associated to these problems. The particular case of the parametric sweeping process involving uniformly subsmooth or uniformly prox-regular sets is studied in details. As an application, we study the sensitivity analysis of the generalized Bolza/Mayer problem governed by a nonsmooth dynamic of a sweeping process type.