Applications of Controlled Sweeping Processes to Nonlinear Crowd Motion Models with Obstacles

TL;DR

This paper extends controlled crowd motion models by incorporating obstacles, developing optimal control solutions for these complex systems, and providing practical examples of the theoretical results.

Contribution

It introduces a novel approach to optimize crowd motion with obstacles using perturbed sweeping processes, advancing the modeling and control techniques in this area.

Findings

Established necessary optimality conditions for the new models

Extended previous models to include obstacle considerations

Provided a practical example demonstrating the approach

Abstract

This paper mainly focuses on solving the dynamic optimization of the planar controlled crowd motion models with obstacles which is an application of a class of optimal control problems governed by a general perturbed nonconvex sweeping process. This can be considered as a significant extension of the previous work regarding the controlled crowd motion models, where the obstacles have not been considered. The necessary optimality conditions for the problem under consideration are established and illustrated by a nontrivial example of practical importance.