A second-order sliding mode controller with integral barrier Lyapunov function for crowd density regulation

Abstract
Effective evacuation strategies are critical for preventing stampedes in large-scale, high-density crowd management. This paper develops a second-order sliding mode controller within a distributed parameter system to regulate crowd density toward a safe reference trajectory, explicitly addressing crowd diffusion dynamics under external disturbances. To guarantee global safety constraints, an integral barrier Lyapunov function is employed to prevent unacceptably high local densities. The entire controller synthesis and stability analysis are conducted within the distributed parameter framework, thereby avoiding errors induced by spatial discretization. Simulation results demonstrate that the proposed controller achieves accurate tracking, reduced chattering, and strict adherence to density bounds, highlighting its potential for real-time evacuation applications.