Necessary conditions for optimal control problems with sweeping systems and end point constraints

TL;DR

This paper extends the Maximum Principle to optimal control problems with sweeping systems and endpoint constraints, using smooth approximations to handle the set constraints.

Contribution

It generalizes previous results by incorporating endpoint constraints into the maximum principle framework for sweeping systems.

Findings

Established necessary conditions for optimality with endpoint constraints.

Extended the maximum principle to a broader class of sweeping control problems.

Utilized smooth approximation techniques for handling set constraints.

Abstract

We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [9] to cover the case where the end point is constrained to take values in a certain set. As in [9], an ingenious smooth approximating family of standard differential equations plays a crucial role.