Saturation control for two dimensional disturbed crowd dynamic system

In this article, a saturation feedback control law is designed for a two dimensional disturbed crowd dynamic system. The disturbances of the system are caused by the influx of unexpected pedestrians. The crowd dynamic system model is based on the conservation law of mass. Control law is designed to make the pedestrians move smoothly in a set direction, and it solves the issue of control saturation successfully. The stability of the closed-loop system is proved by using the Lyapunov method. The modeling of the system and the proof of stability are all done within the scope of the distributed parameter system, avoiding errors caused by the model reduction. Finally, simulation example is used to verify the validity of the control law.