A Nonsmooth Maximum Principle for Optimal Control Problems with State and Mixed Constraints-Convex Case

TL;DR

This paper develops a nonsmooth maximum principle for optimal control problems involving state and mixed constraints, assuming convexity of the velocity set, by combining penalization techniques with recent theoretical results.

Contribution

It introduces a novel nonsmooth maximum principle for constrained optimal control problems under convex velocity set assumptions, integrating penalization and recent mixed constraint theories.

Findings

Derived a new nonsmooth maximum principle for constrained control problems.

Established the importance of convexity in the velocity set for the principle.

Combined penalization techniques with recent theoretical results for mixed constraints.

Abstract

Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known penalization techniques for state constraints together with recent results for mixed constrained problems.