Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908932826464256 |
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| author | Cao, Mina Diagne, Mamadou Shang, Peipei Yu, Lei |
| author_facet | Cao, Mina Diagne, Mamadou Shang, Peipei Yu, Lei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01382 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate Cao, Mina Diagne, Mamadou Shang, Peipei Yu, Lei Optimization and Control Analysis of PDEs Dynamical Systems 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. |
| title | Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate |
| topic | Optimization and Control Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2604.01382 |