Switching Control of Pedestrian Flows Using Discrete Hughes Models

Control of pedestrian flows has various applications such as fire evacuation. Mobile robots play an important role in control of pedestrian flows. In this paper, a switching control method of pedestrian flows is proposed toward using of mobile robots in future. As a mathematical model for pedestrian flows, we adopt the discrete Hughes model, which is a kind of meso-scale models. In the discrete Hughes model, the space is represented as an undirected graph, and pedestrian flows are characterized by changes in density at each vertex. In the proposed method, pedestrian flows are controlled by dynamically switching the graph structure. For each graph structure, a safety penalty is assigned. The optimal switching times that minimize the penalty are determined under a constraint on the exit rate defined in this paper. Through a numerical example, we demonstrate the effectiveness of the proposed method in evacuation guidance.