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arXiv · 2604.01382

Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate

Mina Cao·Mamadou Diagne·Peipei Shang·Lei Yu
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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 $2\times2$ hyperbolic system, covering free and congested flow regimes, respectively, into a shock-free $4\times4$ 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 $H^2$-norm can be stabilized with an arbitrary exponential decay rate via the given feedback controls. Finally, the stabilization results are demonstrated by numerical simulations.

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Mina Cao, Mamadou Diagne, Peipei Shang, Lei Yu. 2026-04-01. Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate. https://arxiv.org/abs/2604.01382

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