Optimal Feedback Control of Pedestrian Flow in Heterogeneous Corridors

Abstract

Maintaining the orderliness and efficiency of pedestrian flow through an architectural area is critical for the evacuation process. Especially, clogs and jams are easily triggered in width-changing areas. In this article, we consider pedestrian movement in heterogeneous corridors and design an optimal feedback control to regulate pedestrian flow. Flow characteristics are first studied based on microscopic social-force simulations. A Gaussian process describes the relationship between flow variables with the observation data. The macroscopic model for flow in heterogeneous corridors is developed. To avoid jams, discharges among these corridors are balanced with the narrowest corridor as the primary concern. At the equilibrium, a continuous-time nonlinear control system is formulated, and the adaptive dynamic programming learns the optimal feedback controller. Policy iteration (PI) and neural networks are combined together, and the convergence of neural-network-based PI is demonstrated by analyzing its equivalence to the Gauss–Newton method. Batch normalization is introduced to stabilize the learning process. Simulated experiments demonstrate that the control design can effectively regulate pedestrian flow for both macroscopic and microscopic models. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The development of video-processing techniques provides a powerful tool to detect human behavior in real time. In crowd events, the pedestrian movement must be regulated; otherwise, it is easy to fall into the faster-is-slower effect. It is especially important for evacuation routes with different widths. In this article, the optimal feedback control is studied to regulate pedestrian flow in heterogeneous corridors. It takes flow densities as state and produces commands that are composed of entrance influx and free-flow velocities. These commands can be executed with the support of speakers, displays, or the recently developed interactive robots. To avoid congestion, discharges of different corridors are balanced, and the system is optimally stabilized at equilibrium. Based on our work, engineers are able to design pedestrian flow control and achieve optimal evacuation in arbitrary heterogeneous corridors.