Mean field games with nonlinear mobilities in pedestrian dynamics

TL;DR

This paper develops a mean-field optimal control model for pedestrian evacuation, linking microscopic behaviors to macroscopic flow, and demonstrates existence, uniqueness, and numerical insights into the model.

Contribution

It introduces a novel mean-field optimal control framework for pedestrian dynamics with nonlinear mobilities, connecting microscopic and macroscopic models.

Findings

Establishment of existence and uniqueness of minimizers.

Connection of the model to Hughes pedestrian flow model.

Numerical simulations illustrating model behavior.

Abstract

In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.