Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

TL;DR

This paper applies a new optimal control theory for sweeping processes to robotic obstacle navigation and traffic flow optimization, enabling efficient solution derivation and complete solution calculation in specific cases.

Contribution

It introduces a novel optimal control approach for perturbed sweeping processes and applies it to practical models in robotics and traffic management.

Findings

Developed procedures for solving optimal control problems in sweeping process models.

Achieved complete calculation of optimal solutions in particular scenarios.

Extended optimal control theory to practical dynamical systems with constraints.

Abstract

The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The first model addresses mobile robot dynamics with obstacles, and the second one concerns control and optimization of traffic flows. Describing these models as controlled sweeping processes with pointwise/hard control and state constraints and applying new necessary optimality conditions for such systems allow us to develop efficient procedures to solve naturally formulated optimal control problems for the models under consideration and completely calculate optimal solutions in particular situations.