Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate
Optimization and Control
2026-04-03 v1 Analysis of PDEs
Dynamical Systems
Abstract
This paper develops boundary feedback controls to stabilize traffic congestion toward a predefined shock equilibrium in the Aw-Rascle-Zhang (ARZ) traffic flow model. We transform the corresponding moving-boundary hyperbolic system, covering free and congested flow regimes, respectively, into a shock-free augmented system on a fixed domain via shock-location-based moving coordinates. By applying the modified Lyapunov functionals concerning shock perturbation, we show that the shock position and the state of the system in -norm can be stabilized with an arbitrary exponential decay rate via the given feedback controls. Finally, the stabilization results are demonstrated by numerical simulations.
Keywords
Cite
@article{arxiv.2604.01382,
title = {Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate},
author = {Mina Cao and Mamadou Diagne and Peipei Shang and Lei Yu},
journal= {arXiv preprint arXiv:2604.01382},
year = {2026}
}