Explicit control law of a coupled reaction–diffusion process

He, Cuihua; Xie, Chunhong; Zhen, Zhiyuan

doi:10.1016/j.jfranklin.2017.01.013

Cited by 7 publications

(5 citation statements)

References 10 publications

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“…Stabilization of the parabolic equations is usually an engineering requirement (E.g., stabilization of temperature in a chemical reaction or biological fermentation). Boundary control to stabilize the parabolic equations is an economical and feasible setting in engineering applications (see, e.g., [2][3][4][5]). It is interested that recently this method is used to globally stabilize the vibrating string system at the equilibrium(see, [6]).…”

Section: Introductionmentioning

confidence: 99%

Local stabilization of semilinear parabolic system by boundary control

Xie

2019

Asian Journal of Control

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This paper addresses local stabilization of a semilinear parabolic system by boundary control. Under a certain assumption on the nonlinearity of the parabolic equation, a linear boundary feedback control law is applied to control the semilinear system. Based on the operator theories and relations of different norms, locally exponential stabilization of the closed loop system is established. Simulations support the established stability result.

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Section: Introductionmentioning

confidence: 99%

Local stabilization of semilinear parabolic system by boundary control

Xie

2019

Asian Journal of Control

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“…In this section, we consider feedback stabilization for system (32). We first introduce a transformation u] in the form 37…”

Section: Observer-based Feedback Designmentioning

confidence: 99%

“…whered x (1, t) contains sufficient estimation of d(t); hence, we use the disturbance estimatord x (1, t) to estimate the disturbance d(t) itself. This is a stabilizing state feedback control for observer (32).…”

Section: Observer-based Feedback Designmentioning

confidence: 99%

“…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 . In the work of Wang et al, boundary state feedback stabilization for a cascade system of an ODE‐heat–ODE‐wave system with external disturbance flowing the control end was discussed by the SMC, which is a variable structure control method.…”

Section: Introductionmentioning

confidence: 99%

“…[25][26][27][28][29] 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. [30][31][32][33][34][35] In the work of Wang et al, 36 boundary state feedback stabilization for a cascade system of an ODE-heat-ODE-wave system with external disturbance flowing the control end was discussed by the SMC, which is a variable structure control method.…”

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confidence: 99%

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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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Local exponential stabilization of a coupled ODE-Fisher’s PDE system

Ayadi

Mahfoudhi

2023

European Journal of Control

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Explicit control law of a coupled reaction–diffusion process

Cited by 7 publications

References 10 publications

Local stabilization of semilinear parabolic system by boundary control

Local stabilization of semilinear parabolic system by boundary control

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

Local exponential stabilization of a coupled ODE-Fisher’s PDE system

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