Optimization of Controlled Free-Time Sweeping Processes with Applications to Marine Surface Vehicle Modeling

TL;DR

This paper develops a finite-difference approximation method for solving free-time optimal control problems in sweeping processes, with applications demonstrated on marine surface vehicle models.

Contribution

It introduces a constructive approximation procedure and derives necessary optimality conditions for discrete solutions in sweeping process control problems.

Findings

Established necessary optimality conditions for discrete solutions

Applied the method to a marine surface vehicle control model

Demonstrated the effectiveness of the approximation procedure

Abstract

The paper is devoted to a free-time optimal control problem for sweeping processes. We develop a constructive finite-difference approximation procedure that allows us to establish necessary optimality conditions for discrete optimal solutions and then show how these optimality conditions are applied to solving a controlled marine surface vehicle model.