Optimal control of nonconvex sweeping processes with separable endpoints: Nonsmooth maximum principle for local minimizers

Abstract

In this paper the nonsmooth maximum principle derived in [33] for global minimizers of an optimal control problem governed by a controlled nonconvex sweeping process, is generalized in several directions. More specifically, the assumptions are weakened, a state final-endpoint constraint set is added, the cost function is allowed to depend on both endpoints of the state, strong local minimizers are considered, and new subdifferentials that are strictly smaller than Clarke and Mordukhovich subdifferentials are employed.