Feedback Control of Crowd Evacuation in One Dimension

This paper studies crowd models in one dimension. The focus of this paper is on the design of nonlinear feedback controllers for these models. Two different models are studied where dynamics are represented by a single partial differential equation (PDE) in one case and a system of hyperbolic PDEs in another, and control models are proposed for both. These include advective, diffusive, and advective-diffusive controls. The models representing evacuation dynamics are based on the laws of conservation of mass and momentum and are described by nonlinear hyperbolic PDEs. As such, the system is distributed in nature. We address the design of feedback control for these models in a distributed setting where the problem of control and stability is formulated directly in the framework of PDEs. The control goal is to design feedback controllers to control the movement of people during evacuation and avoid jams and shocks.