On a mean field game optimal control approach modeling fast exit scenarios in human crowds

Martin Burger, Marco Di Francesco, Peter A. Markowich, Marie Therese Wolfram

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations

Abstract

The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. 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 and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.
Original languageEnglish (US)
Title of host publication52nd IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages3128-3133
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - Dec 2013

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