Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 56, Issue 1, Pages 434-455Publisher
SIAM PUBLICATIONS
DOI: 10.1137/17M1119196
Keywords
crowd dynamics; crowd aversion; mean-field approximation; interacting populations; optimal control; mean-field type game
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Funding
- Swedish Research Council [2016-04086]
- Swedish Research Council [2016-04086] Funding Source: Swedish Research Council
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We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572-1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a personal space where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.
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