PI controllers for the general Saint-Venant equations

Hayat, Amaury

doi:10.48550/arxiv.2108.02703

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…Different from [6] or [13], as the extra integral terms need to be processed, we shall consider the items of z i . Inspired by [24,26], we consider the Lyapunov function candidate as the following…”

Section: A Lyapunov Function For the Linearized Cascade Systemmentioning

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: A Lyapunov Function For the Linearized Cascade Systemmentioning

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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“…Here, we focus on damping stabilization where damping terms can be regarded as a simple local feedback law, despite various other powerful stabilization techniques in the literature. These methods usually provide more complicated nonlocal feedback laws, which include but are not limited to, the backstepping method [11,12,19], the basic Lyapunov approach for systems of conservation laws [21], the frequency Lyapunov for finite time stabilization problems [50], and [26] for the focusing NLKG.…”

Section: Theorem 12 (Low-energy Exact Controllability Of Wave Maps)mentioning

confidence: 99%

Semi-global controllability of a geometric wave equation

Krieger¹,

Xiang²

2022

Preprint

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We prove the semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain S 1 and target S k . First we show that damping stabilizes the system when the energy is strictly below the threshold 2π, where harmonic maps appear as obstruction for global stabilization. Then, we adapt an iterative control procedure to get low-energy exact controllability of the wave maps equation. This result is optimal in the case k = 1.

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“…Finally, in view of the recent progresses in stabilization problems, see for instance [11,17,18], it also sounds interesting to have a look at the related stabilization problems.…”

Section: 3mentioning

confidence: 99%

On the global approximate controllability in small time of semiclassical 1-D Schrödinger equations between two states with positive quantum densities

Coron¹,

Xiang²,

Zhang³

2021

Preprint

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In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schrödinger equation with two controls between two states with positive quantum densities. We first control the asymptotic expansions of the zeroth and first order of the physical observables via Agrachev-Sarychev's method. Then we conclude the proof through techniques of semiclassical approximation of the nonlinear Schrödinger equation.

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PI controllers for the general Saint-Venant equations

Cited by 4 publications

References 25 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

Semi-global controllability of a geometric wave equation

On the global approximate controllability in small time of semiclassical 1-D Schrödinger equations between two states with positive quantum densities

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