The Stabilization of a One-Dimensional Wave Equation by Boundary Feedback With Noncollocated Observation

Guo, Bao‐Zhu; Xu, Cheng-Zhong

doi:10.1109/tac.2006.890385

Cited by 103 publications

(51 citation statements)

References 21 publications

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“…In the last few years, special attentions have been paid to the boundary feedback control for the non-collocated or unstable wave and beam equations. An observer-based compensator which exponentially stabilizes the string system with a non-collocated actuator/sensor configuration is proposed in [5]. In [3], the controller and observer are designed using the backstepping method to exponentially stabilize a one-dimensional wave equation that contains destabilizing anti-stiffness boundary condition at its free end.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation and stabilization for an unstable one-dimensional wave equation with boundary input harmonic disturbances

Guo

2012

2012 American Control Conference (ACC)

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This paper is concerned with the parameter estimation and stabilization of a one-dimensional wave equation with instability suffered at one end and uncertainty of harmonic disturbances at the controlled end. An adaptive observer is designed in terms of measured position at one end and velocity at the other end. The backstepping method for infinite-dimensional system is adopted in the design of the feedback law. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity.

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Section: Introductionmentioning

confidence: 99%

Parameter estimation and stabilization for an unstable one-dimensional wave equation with boundary input harmonic disturbances

Guo

2012

2012 American Control Conference (ACC)

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“…Moreover, the closed-loop form of a non-collocated system is usually non-dissipative which makes the traditional Lyapunov method hard to apply to the analysis of its stability. For recent progresses on non-collocated control, we refer to Deguenon, Geguenon, Sallet, and Xu (2006), Guo and Xu (2007), Krstic, Guo, Balogh, and Smyshlyaev (2008) and Smyshlyaev and Kristic (2005).…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation and stabilisation for a one-dimensional wave equation with boundary output constant disturbance and non-collocated control

Guo

2011

International Journal of Control

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“…Recently, inspired by the works of [7,19], we solved successfully the stabilization of one dimensional wave and beam equations with boundary control and non-collocated observation [12,14]. The generalization to multidimensional systems is also available [11].…”

Section: Introductionmentioning

confidence: 99%

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Guo

Hammouri

2010

ESAIM: COCV

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Abstract.The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the boundary observation suffers from an arbitrary long time delay. We use the observer and predictor to solve the problem: The state is estimated in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. It is shown that the estimator/predictor based state feedback law stabilizes the delay system asymptotically or exponentially, respectively, relying on the initial data being non-smooth or smooth. Numerical simulations are presented to illustrate the effect of the stabilizing controller.Mathematics Subject Classification. 35B37, 93B52, 93C05, 93C20, 93D15.

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The Stabilization of a One-Dimensional Wave Equation by Boundary Feedback With Noncollocated Observation

Cited by 103 publications

References 21 publications

Parameter estimation and stabilization for an unstable one-dimensional wave equation with boundary input harmonic disturbances

Parameter estimation and stabilization for an unstable one-dimensional wave equation with boundary input harmonic disturbances

Parameter estimation and stabilisation for a one-dimensional wave equation with boundary output constant disturbance and non-collocated control

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

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