Non-separable mean field games for pedestrian flow: Generalized hughes model

In this paper, we present a new generalized Hughes model designed to intelligently depict pedestrian congestion dynamics, allowing pedestrian groups to either navigate through or circumvent high-density regions. First, we describe the microscopic settings of the model. The corresponding optimization problems are deterministic and can be formulated by a closed-loop model predictive control strategy. This microscopic setup leads in the mean-field limit to the generalized Hughes model which is a class of non-separable mean field games system, i.e. Fokker-Planck equation and viscous Hamilton-Jacobi-Bellman equation are coupled in a forward-backward structure. We provide an overview of mean field games related to our intelligent fluid model. Additionally, we show the existence of weak solutions to the generalized Hughes model and analyze the vanishing-viscosity limit of weak solutions. Finally, we conduct various numerical experiments to demonstrate the generalized Hughes model.