Sliding Mode Control of Crowd Dynamics

In this paper, the design of nonlinear sliding mode controllers for models representing crowd dynamics in one dimension is presented. The main contribution of this paper is the stability analysis and robust control synthesis of hyperbolic partial differential equation (PDE) system models using the sliding mode method. The application of this research is in crowd control and in dynamically controlling the evacuation of pedestrians in the presence of disturbances. Crowd densities can change due to blocked exits or due to a varying influx of people. Recent advances in sensor technology have made the measurement of pedestrian densities and velocities possible. As such, the development and implementation of efficient control algorithms to control crowd movements that can avoid jams is realizable. The crowd model presented here is a system of nonlinear hyperbolic PDEs based on the laws of conservation of mass and momentum. The sliding mode control is designed in the presence of both matched and unmatched uncertainties due to external disturbance and parametric variations. The controllers designed are shown to be robust to disturbances.