Feedback control design of crowd evacuation system based on the diffusion model

This paper pertains to the study of feedback control design for the crowd evacuation in the framework of 1D and 2D models, respectively. The models representing crowd dynamics are based on the conservation law of mass with the density and velocity relationship given by a diffusion model. The feedback controllers taking care of control saturation are designed by using the method of feedback linearization for partial differential equations, which can keep the pedestrians evacuating in specific direction and fixed speed. By constructing the corresponding Lyapunov functional, the stability of the closed-loop system under the designed distributed feedback controller is proved. Finally, an example is given to illustrate the results.