Boundary Observer for Congested Freeway Traffic State Estimation via Aw-Rascle-Zhang model

TL;DR

This paper introduces a boundary observer for estimating congested freeway traffic states using the Aw-Rascle-Zhang PDE model, enabling real-time traffic monitoring from limited boundary measurements.

Contribution

It develops a novel boundary observer design for the nonlinear ARZ traffic model using PDE backstepping, ensuring exponential stability and finite-time convergence.

Findings

Observer accurately estimates traffic states in simulations.

Ensures exponential stability of the estimation error.

Validates effectiveness without initial condition knowledge.

Abstract

This paper develops boundary observer for estimation of congested freeway traffic states based on Aw-Rascle-Zhang(ARZ) partial differential equations (PDE) model. Traffic state estimation refers to 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 boundary observer design so that estimates of aggregated traffic states in a freeway segment are obtained simply from boundary measurement of flow and velocity. The macroscopic traffic dynamics is represented by the ARZ model, consisting of $2 \times 2$ coupled nonlinear hyperbolic PDEs for traffic density and velocity. Analysis of the linearized ARZ model leads to the study of a hetero-directional hyperbolic PDE model for congested traffic regime. Using spatial transformation and PDE backstepping method, we construct a boundary observer with a copy of the nonlinear plant and output injection of boundary measurement errors. The output injection gains are designed for the error system of the linearized ARZ model so that the exponential stability of error system in the $L^2$ norm and finite-time convergence to zero are guaranteed. Simulations are conducted to validate the boundary observer design for nonlinear ARZ model without knowledge of initial conditions.