Feedback control of macroscopic crowd dynamic models

This paper presents design of nonlinear feedback controllers for two different macroscopic models for two- dimensional pedestrian dynamics. The models presented here are based on the laws of conservation of mass and momentum. These models have been developed by extending one-dimension macroscopic vehicle traffic flow models that use two-coupled partial deferential equations (PDEs). These models modify the vehicle traffic models so that bi-directional controlled flow is possible. Both models satisfy the conservation principle and are classified as nonlinear, time-dependent, hyperbolic PDE systems. The equations of motion in both cases are described by nonlinear partial differential equations. We address the feedback control problem for both models in the framework of partial differential equations. The objective is to synthesize nonlinear distributed feedback controllers that guarantee stability of a closed loop system.