Nonsmooth mean field games with state constraints - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2022

Nonsmooth mean field games with state constraints

(1, 2) , (2)
1
2

Abstract

In this paper, we consider a mean field game model inspired by crowd motion where agents aim to reach a closed set, called target set, in minimal time. Congestion phenomena are modeled through a constraint on the velocity of an agent that depends on the average density of agents around their position. The model is considered in the presence of state constraints: roughly speaking, these constraints may model walls, columns, fences, hedges, or other kinds of obstacles at the boundary of the domain which agents cannot cross. After providing a more detailed description of the model, the paper recalls some previous results on the existence of equilibria for such games and presents the main difficulties that arise due to the presence of state constraints. Our main contribution is to show that equilibria of the game satisfy a system of coupled partial differential equations, known mean field game system, thanks to recent techniques to characterize optimal controls in the presence of state constraints. These techniques not only allow to deal with state constraints but also require very few regularity assumptions on the dynamics of the agents.
Fichier principal
Vignette du fichier
main.pdf (809.21 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03409027 , version 1 (29-10-2021)
hal-03409027 , version 2 (12-08-2022)

Identifiers

Cite

Saeed Sadeghi Arjmand, Guilherme Mazanti. Nonsmooth mean field games with state constraints. ESAIM: Control, Optimisation and Calculus of Variations, 2022, 28, Paper No. 74, 42 pp. ⟨10.1051/cocv/2022069⟩. ⟨hal-03409027v2⟩
63 View
30 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More