Robust Boundary Observer for Traffic State Estimation on One Incoming and Two Outgoing Roads

Abstract

In this paper we design a partial differential equation (PDE) observer for state estimation of a fundamental component of traffic flow network: one incoming road segment and two outgoing road segment connected by a junction. Traffic state estimation refers to acquisition of traffic state information from partially observed traffic data. We propose a PDE model-based observer to estimate traffic density and velocity on the ”Y” shape traffic network from boundary sensing at the nodes including inlet, outlet and middle junction. The macroscopic traffic dynamics on each road segment are governed by Aw-Rascle-Zhang (ARZ) model, consisting of second-order nonlinear PDEs of traffic density and velocity. Using PDE backstepping method, we first construct a boundary observer from a copy of the plant and output injections from boundary measurement errors of the middle junction. The exponential stability of the estimation error system to zero in the L 2 norm is achieved. For robustness of the observer design, we prove the Input-to-State Stability (ISS) of the estimation error system with respect to in-domain spatially distributed disturbances and measurement noise.