Moving Boundary Observer for Traffic State Estimation with Shock Waves

Abstract

Traffic state estimation is the acquisition of traffic state information from partially observed traffic data, which is crucial to the effectiveness of traffic management and control. This paper investigates the estimation problem of traffic flow state with shock waves in the congestion regime by proposing a moving boundary observer. 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 shock waves is proposed. We propose a moving boundary observer that can estimate the aggregated traffic state by simply measuring the average vehicle velocity at the moving interface of the shock wave. The observer system is constructed from a copy of the plant and by incorporating injections from moving boundary output measurement errors, in which the observer gains are obtained based on the PDE backstepping method. The exponential stability of the observer error system in the L2 norm is proved via Lyapunov analysis. Finally, the validity of the moving boundary observer for traffic state estimation with shock waves is verified by numerical simulations.