OPTIMAL CONTROL OF THE SWEEPING PROCESS WITH A NONSMOOTH MOVING SET

In this paper we prove a fully nonsmooth Pontryagin maximum principle for optimal control problems driven by a sweeping process with drift x is an element of f(t, x, u) -N-C(t)(x). The setting we study is an optimal control problem of Mayer type in which the optimization procedure is carried out by choosing a control function u(t) from a class of admissible controls U. The choice of u is an element of U modifies the drift f and the related solution x(t) to the perturbed sweeping process. Here, for the first time, we are able to prove a Pontryagin maximum principle in the case in which the moving set C(t) is both nonsmooth and nonconvex by using a novel exact penalization technique which is able to exploit the controllability properties of the dynamics.

Automated summary

In this paper, we prove a fully nonsmooth Pontryagin maximum principle for optimal control problems driven by a sweeping process with drift term x is an element of f(t, x, u) -N-C(t)(x). The novel exact penalization technique is used to exploit the controllability properties of the dynamics and prove the maximum principle in the case when the moving set C(t) is both nonsmooth and nonconvex.