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

Handle URI:
http://hdl.handle.net/10754/564822
Title:
On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Authors:
Burger, Martin; Di Francesco, Marco; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Wolfram, Marie Therese
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.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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
Issue Date:
Dec-2013
DOI:
10.1109/CDC.2013.6760360
Type:
Conference Paper
ISSN:
01912216
ISBN:
9781467357173
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBurger, Martinen
dc.contributor.authorDi Francesco, Marcoen
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorWolfram, Marie Thereseen
dc.date.accessioned2015-08-04T07:17:16Zen
dc.date.available2015-08-04T07:17:16Zen
dc.date.issued2013-12en
dc.identifier.isbn9781467357173en
dc.identifier.issn01912216en
dc.identifier.doi10.1109/CDC.2013.6760360en
dc.identifier.urihttp://hdl.handle.net/10754/564822en
dc.description.abstractThe 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.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleOn a mean field game optimal control approach modeling fast exit scenarios in human crowdsen
dc.typeConference Paperen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal52nd IEEE Conference on Decision and Controlen
dc.conference.date10 December 2013 through 13 December 2013en
dc.conference.name52nd IEEE Conference on Decision and Control, CDC 2013en
dc.conference.locationFlorenceen
dc.contributor.institutionInstitute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, 48149 Münstere, Germanyen
dc.contributor.institutionDepartment of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdomen
dc.contributor.institutionDepartment of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austriaen
kaust.authorMarkowich, Peter A.en
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