PDE Traffic Observer Validated on Freeway Data

Abstract

This article develops a boundary observer for the estimation of congested freeway traffic states based on the Aw-Rascle-Zhang (ARZ) partial differential equations (PDEs) model. Traffic state estimation refers to the acquisition of traffic state information from partially observed traffic data. This problem is relevant for freeway due to its limited accessibility to real-time traffic information. We propose a model-driven approach in which the estimation of aggregated traffic states in a freeway segment is obtained simply from the boundary measurement of flow and velocity without knowledge of the initial states. The macroscopic traffic dynamics is represented by the ARZ model, a 2 ×2 coupled nonlinear hyperbolic PDEs for traffic density and velocity. Using the PDE backstepping method, we construct a boundary observer consisting of a copy of the nonlinear plant with output injections from boundary measurement errors. The exponential stability of the estimation error system in the L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> norm and finite-time convergence to zero is guaranteed. Numerical simulation and data validation are conducted to validate the boundary observer design with vehicle trajectory data.