Mean field games with nonlinear mobilities in pedestrian dynamics
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractIn 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 the 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.
SponsorsMTW acknowledges financial support of the Austrian Science Foundation FWF via the Hertha Firnberg Project T456-N23. MDF is supported by the FP7-People Marie Curie CIG (Career Integration Grant) Diffusive Partial Differential Equations with Nonlocal Interaction in Biology and Social Sciences (DifNonLoc), by the 'Ramon y Cajal' sub-programme (MICINN-RYC) of the Spanish Ministry of Science and Innovation, Ref. RYC-2010-06412, and by the by the Ministerio de Ciencia e Innovacion, grant MTM2011-27739-C04-02. The authors thank the anonymous referees for useful comments to improve the manuscript.