English

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 2×22\times2 hyperbolic system, covering free and congested flow regimes, respectively, into a shock-free 4×44\times4 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 H2H^2-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}
}