Boundary stabilization of 1D hyperbolic systems

Hayat, Amaury

doi:10.1016/j.arcontrol.2021.10.009

Cited by 7 publications

(2 citation statements)

References 137 publications

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“…The semilinear system with Lipschitz source term was treated in [23] and the nonlinear system in the framework of the C 1 norm in [7]. One can refer to [28] (see also [22]) for an overview of the ISS for PDEs.…”

Section: Introductionmentioning

confidence: 99%

PI Control for the Cascade Channels Modeled by General Saint-Venant Equations

Hayat,

Hu,

Shang

2024

IEEE Trans. Automat. Contr.

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The Input-to-State Stability of the non-horizontal cascade channels with different arbitrary cross section, slope and friction modeled by Saint-Venant equations is addressed in this paper. The control input and measured output are both on the collocated boundary. The PI control is proposed to study both the exponential stability and the output regulation of the closed-loop systems with the aid of Lyapunov approach. An explicit quadratic Lyapunov function as a weighted function of a small perturbation of the non-uniform steady-states of different channels is constructed. We show that by a suitable choice of the boundary feedback controls, the local exponential stability and the Input-to-State Stability of the nonlinear Saint-Venant equations for the H 2 norm are guaranteed, then validated with numerical simulations. Meanwhile, the output regulation and the rejection of constant disturbances are realized as well.

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Section: Introductionmentioning

confidence: 99%

PI Control for the Cascade Channels Modeled by General Saint-Venant Equations

Hayat,

Hu,

Shang

2024

IEEE Trans. Automat. Contr.

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“…Systems of transport equations have received much attention for many years due to the many physical phenomena they model: e.g pressure drilling 4 , water management systems 5 , aeronomy 6 and cable vibration dynamics 7 . A good overview of the actual research lines concerning this topic is provided in 8 and 9 .…”

Section: Introductionmentioning

confidence: 99%

Active disturbance rejection control for the stabilization of a linear hyperbolic system

Balogoun,

Marx,

Orlov

et al. 2023

Preprint

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This paper deals with the stabilization of a linear hyperbolic system subject to a boundary disturbance. Our feedback design relies on the strategy called active disturbance rejection control (ADRC). The unknown disturbance is estimated by an extended state observer. We prove the existence of solutions of the closed-loop system and the global asymptotic stability of the closed-loop system. A numerical example is given to illustrate the efficiency of our strategy.

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Boundary Stabilization of Complex Coupled Hyperbolic Stochastic Systems

Gao,

Jia,

et al. 2024

Lecture Notes in Computer Science

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Boundary stabilization of 1D hyperbolic systems

Cited by 7 publications

References 137 publications

PI Control for the Cascade Channels Modeled by General Saint-Venant Equations

PI Control for the Cascade Channels Modeled by General Saint-Venant Equations

Active disturbance rejection control for the stabilization of a linear hyperbolic system

Boundary Stabilization of Complex Coupled Hyperbolic Stochastic Systems

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