On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Type
Conference PaperKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2013-12Permanent link to this record
http://hdl.handle.net/10754/564822
Metadata
Show full item recordAbstract
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.2013.6760360Conference/Event name
52nd IEEE Conference on Decision and Control, CDC 2013ISBN
9781467357173ae974a485f413a2113503eed53cd6c53
10.1109/CDC.2013.6760360