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

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    Type
    Conference Paper
    Authors
    Burger, Martin
    Di Francesco, Marco
    Markowich, Peter A. cc
    Wolfram, Marie Therese
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2013-12
    Permanent link to this record
    http://hdl.handle.net/10754/564822
    
    Metadata
    Show full item record
    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.
    Citation
    Burger, M., Di Francesco, M., Markowich, P. A., & Wolfram, M.-T. (2013). On a mean field game optimal control approach modeling fast exit scenarios in human crowds. 52nd IEEE Conference on Decision and Control. doi:10.1109/cdc.2013.6760360
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    52nd IEEE Conference on Decision and Control
    Conference/Event name
    52nd IEEE Conference on Decision and Control, CDC 2013
    ISBN
    9781467357173
    DOI
    10.1109/CDC.2013.6760360
    ae974a485f413a2113503eed53cd6c53
    10.1109/CDC.2013.6760360
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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