PI Boundary Feedback Control for Freeway Traffic Networks

This paper investigates the proportional-integral (PI) boundary feedback control for freeway traffic networks, where the control and output measures are located at the boundaries. The boundary conditions of the vehicle transportation system are subject to unknown constant disturbances. Combing Aw-Rascle (AR) traffic flow model and Riemann invariants approach, we use the integration of on-ramp metering and variable speed limit control as PI boundary controller to address the issues of feedback stabilization and disturbance rejection. To this end, we deduce the stabilizing control laws and propose the stability condition which can extended to a general class of hyperbolic systems including the freeway networks. The exponential convergence of the traffic flow dynamics is achieved and validated with numerical simulation.