Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation

Shuxia Tang; Miroslav Krstic

doi:10.1109/ACC.2015.7171020

Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation

Shuxia Tang, Miroslav Krstic

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

This paper addresses the problem of stabilizing a class of one-dimensional linearized Korteweg-de Vries systems with possible anti-diffusion (LKdVA for short), through control at one end and non-collocated observation at the other end. An exponentially convergent observer is designed, and then a dynamical stabilizing output feedback boundary controller is constructed based on the observer. The resulting closed-loop systems can achieve arbitrary exponential decay rate. In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper.

Original language	English
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1959-1964
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7171020
State	Published - Jul 28 2015
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: Jul 1 2015 → Jul 3 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	07/1/15 → 07/3/15

Keywords

Anti-diffusion
Backstepping
Linearized Korteweg-de Vries systems
Observer
Output feedback

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10.1109/ACC.2015.7171020

Cite this

Tang, S., & Krstic, M. (2015). Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation. In ACC 2015 - 2015 American Control Conference (pp. 1959-1964). Article 7171020 (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7171020

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title = "Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation",

abstract = "This paper addresses the problem of stabilizing a class of one-dimensional linearized Korteweg-de Vries systems with possible anti-diffusion (LKdVA for short), through control at one end and non-collocated observation at the other end. An exponentially convergent observer is designed, and then a dynamical stabilizing output feedback boundary controller is constructed based on the observer. The resulting closed-loop systems can achieve arbitrary exponential decay rate. In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper.",

keywords = "Anti-diffusion, Backstepping, Linearized Korteweg-de Vries systems, Observer, Output feedback",

author = "Shuxia Tang and Miroslav Krstic",

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Tang, S & Krstic, M 2015, Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation. in ACC 2015 - 2015 American Control Conference., 7171020, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 1959-1964, 2015 American Control Conference, ACC 2015, Chicago, United States, 07/1/15. https://doi.org/10.1109/ACC.2015.7171020

Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation. / Tang, Shuxia; Krstic, Miroslav.
ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1959-1964 7171020 (Proceedings of the American Control Conference; Vol. 2015-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Krstic, Miroslav

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N2 - This paper addresses the problem of stabilizing a class of one-dimensional linearized Korteweg-de Vries systems with possible anti-diffusion (LKdVA for short), through control at one end and non-collocated observation at the other end. An exponentially convergent observer is designed, and then a dynamical stabilizing output feedback boundary controller is constructed based on the observer. The resulting closed-loop systems can achieve arbitrary exponential decay rate. In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper.

AB - This paper addresses the problem of stabilizing a class of one-dimensional linearized Korteweg-de Vries systems with possible anti-diffusion (LKdVA for short), through control at one end and non-collocated observation at the other end. An exponentially convergent observer is designed, and then a dynamical stabilizing output feedback boundary controller is constructed based on the observer. The resulting closed-loop systems can achieve arbitrary exponential decay rate. In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper.

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KW - Backstepping

KW - Linearized Korteweg-de Vries systems

KW - Observer

KW - Output feedback

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EP - 1964

BT - ACC 2015 - 2015 American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

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Y2 - 1 July 2015 through 3 July 2015

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Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation

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