Control of PDE–ODE cascades with Neumann interconnections

Susto, Gian Antonio; Krstić, Miroslav

doi:10.1016/j.jfranklin.2009.09.005

Cited by 204 publications

(10 citation statements)

References 23 publications

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“…This trend is driven by a number of engineering applications such flexible aircraft [29], flexible cranes [17], power converters connected to transmission lines [13], and solid-gas interaction of heat diffusion and chemical reaction [38]. Coupled PDE and ODE dynamics also arise due to actuator and sensor dynamics employed to implement feedback control strategies [23,36]. For instance, the PDE can represent the open-loop plant while the ODE part gathers actuator/sensor dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The state-feedback stabilization and the observer design of a diffusion PDE cascaded with an ODE was solved using backstepping design in [23,36]. These control design approaches, which can be seen as the generalization of predictor feedback techniques [19] as they aim at compensating an infinite-dimensional input dynamics [24], have then been extended to the statefeedback stabilization of other systems described by PDEs such as strings [22,36] and linearized Korteweg-de Vries equation [3].…”

Section: Introductionmentioning

confidence: 99%

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Output feedback stabilization of an ODE-Reaction–Diffusion PDE cascade with a long interconnection delay

Lhachemi

Shorten

2023

Automatica

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Output feedback stabilization of an ODE-Reaction–Diffusion PDE cascade with a long interconnection delay

Lhachemi

Shorten

2023

Automatica

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“…On the other hand, there are many cascade ODE‐PDE systems that appeared in engineering applications such as mechanical coupling, electromagnetic coupling, and coupled chemical reactions . An ODE‐heat system, an ODE‐wave system, an ODE‐beam system, and an ODE coupled with a semilinear scalar parabolic PDE without considering the boundary disturbance have also been considered .…”

Section: Introductionmentioning

confidence: 99%

Output feedback stabilization for a cascaded heat PDE‐ODE system subject to uncertain disturbance

Jia

Liu

2018

Intl J Robust & Nonlinear

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Summary In this paper, we are concerned with the output feedback exponential stabilization of a cascaded parabolic partial differential equation–ordinary differential equation system where the control end suffers from the external uncertain disturbance. We design an unknown input–type state observer with the disturbance estimator term, which is used to stabilize this cascaded system and compensate the external disturbance simultaneously. The stabilizing state feedback control is designed for the observer system by the three‐step backstepping transformation, which is the corresponding observer‐based output feedback stabilizing control for the original system. Finally, the closed‐loop system is shown to be exponentially stable.

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“…The controllability problem of coupled PDE-ODE systems has been discussed in [23] and [26]. Many problems of stabilization for a class of linear coupled PDE-ODE have been solved [22], [21], [20], [11], [19], [27], to name just a few. Some nonlinear extensions are studied in [24], [1], [5] where the non linearity is assumed to be globally Lipschitz, and in [2], [8], [9], [4] for general nonlinear ODE.…”

mentioning

confidence: 99%

Rapid exponential stabilization by boundary state feedback for a class of coupled nonlinear ODE and $ 1-d $ heat diffusion equation

Benabdallah¹,

Dlala²

2022

DCDS-S

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<p style='text-indent:20px;'>In this paper, we solve the problem of rapid exponential stabilization for coupled nonlinear ordinary differential equation (ODE) and <inline-formula><tex-math id="M2">\begin{document}$ 1-d $\end{document}</tex-math></inline-formula> unstable linear heat diffusion. The control acts at a boundary of the heat domain and the heat equation enters in the ODE by Dirichlet connection. We show that the infinite dimensional backstepping transformation introduced recently for stabilization of coupled linear ODE-PDE can deal with a nonlinear ODE and obtain a global stabilization result. Our result is innovative and no similar result can be found in the literature as it combines the three following factors, i) nonlinear term in the ODE subsystem, ii) unstable PDE subsystem and iii) mixed boundary condition. Not only this, the techniques used in this work can provide answers to fundamental questions, such as the stabilization of coupled systems where both subsystems may contain nonlinear terms.</p>

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Control of PDE–ODE cascades with Neumann interconnections

Cited by 204 publications

References 23 publications

Output feedback stabilization of an ODE-Reaction–Diffusion PDE cascade with a long interconnection delay

Output feedback stabilization of an ODE-Reaction–Diffusion PDE cascade with a long interconnection delay

Output feedback stabilization for a cascaded heat PDE‐ODE system subject to uncertain disturbance

Rapid exponential stabilization by boundary state feedback for a class of coupled nonlinear ODE and $ 1-d $ heat diffusion equation

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