Applications of Optimal Control of a Nonconvex Sweeping Process to Optimization of the Planar Crowd Motion Model

TL;DR

This paper develops optimal control methods for a nonconvex sweeping process and applies them to optimize a planar crowd motion model, providing analytical solutions for simple cases and advancing traffic equilibrium analysis.

Contribution

It introduces new theoretical results for controlling nonconvex sweeping processes and applies them to solve a microscopic crowd motion optimization problem analytically.

Findings

Analytical solution for two-participant crowd motion model

Theoretical framework for nonconvex sweeping process control

Enhanced understanding of traffic equilibrium dynamics

Abstract

This paper concerns optimal control of a nonconvex perturbed sweeping process and its applications to optimization of the planar crowd motion model of traffic equilibria. The obtained theoretical results allow us to investigate a dynamic optimization problem for the microscopic planar crown motion model with finitely many participants and completely solve it analytically in the case of two participants.