Observer-Based Output Feedback Stabilization for Stop-and-Go Waves of Vehicle Traffic Flow

This paper designs an observer-based output feedback controller for traffic flow with stop-and-go waves and disturbances in order to dissipate traffic congestion. The macroscopic traffic flow dynamics in the congestion regime is described by the linearized Aw-Rascle-Zhang (ARZ) traffic flow model over a time-varying moving spatial domain, and according to the Rankine-Hugoniot condition and the characteristic velocities of the ARZ model, a novel propagation model of the stop-and-go waves is proposed. To stabilize the traffic state and the stop-and-go waves, and to suppress traffic disturbances, an observer-based output feedback controller is designed by using the PDE backstepping method. The controller utilizes the estimated state of an observer, which is constructed based on boundary measurements only. The exponential stability of the closed-loop system in the
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norm is proved by the Lyapunov analysis. Finally, the effectiveness of the controller for stabilizing the traffic state with stop-and-go waves and disturbances is verified by numerical simulations.