Adaptive boundary observer for ARZ traffic flow model with domain and boundary uncertainties

This paper studies the problem of the adaptive boundary observer design for the Aw-Rascle-Zhang (ARZ) traffic flow model, which is subject to both relaxation time uncertainty in the domain and boundary input disturbance. The boundary input disturbance comes from merging vehicles' velocities at the downstream on-ramp, and we scale the disturbance by a low-pass filter based on the ordinary differential equation (ODE). Then, the ARZ model with the domain uncertainty and boundary input disturbance can be linearized to a coupled ODEPDE system. Based on the swapping transformation, an adaptive boundary observer with least-squares type parameter estimation is designed to estimate the traffic states, the domain uncertainty, and the boundary input disturbance, simultaneously. The exponential convergence conditions w.r.t. observer feedback gains are given by employing the Lyapunov technique. Finally, the simulation results are presented to illustrate the effectiveness of the designed adaptive boundary observer.