Stabilization of linearized Korteweg-de Vries systems with anti-diffusion

Shuxia Tang; Miroslav Krstic

Stabilization of linearized Korteweg-de Vries systems with anti-diffusion

Shuxia Tang, Miroslav Krstic

Mechanical Engineering

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

11 Scopus citations

Abstract

In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve arbitrary exponential decay rate. Semigroup of linear operators is constructed in analyzing well-posedness and stability of the target systems, and mathematical induction is used in proving existence of kernel functions. An example is also presented, which illustrates performance of the controller. The decay rate estimate derived in this paper is not necessarily equal to decay rate, which can be seen from the appendix.

Original language	English
Title of host publication	2013 American Control Conference, ACC 2013
Pages	3302-3307
Number of pages	6
State	Published - 2013
Event	2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: Jun 17 2013 → Jun 19 2013

Publication series

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

Conference

Conference	2013 1st American Control Conference, ACC 2013
Country	United States
City	Washington, DC
Period	06/17/13 → 06/19/13

Keywords

Antidiffusion
Arbitrary exponential decay rate
Backstepping
Linearized Korteweg-de Vries systems
Semigroup of linear operators

Access to Document

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Stabilization of linearized Korteweg-de Vries systems with anti-diffusion'. Together they form a unique fingerprint.

Cite this

@inproceedings{f0a4e72082a4459ba156a91fa34f827d,

title = "Stabilization of linearized Korteweg-de Vries systems with anti-diffusion",

abstract = "In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve arbitrary exponential decay rate. Semigroup of linear operators is constructed in analyzing well-posedness and stability of the target systems, and mathematical induction is used in proving existence of kernel functions. An example is also presented, which illustrates performance of the controller. The decay rate estimate derived in this paper is not necessarily equal to decay rate, which can be seen from the appendix.",

keywords = "Antidiffusion, Arbitrary exponential decay rate, Backstepping, Linearized Korteweg-de Vries systems, Semigroup of linear operators",

author = "Shuxia Tang and Miroslav Krstic",

year = "2013",

language = "English",

isbn = "9781479901777",

series = "Proceedings of the American Control Conference",

pages = "3302--3307",

booktitle = "2013 American Control Conference, ACC 2013",

}

TY - GEN

T1 - Stabilization of linearized Korteweg-de Vries systems with anti-diffusion

AU - Tang, Shuxia

AU - Krstic, Miroslav

PY - 2013

Y1 - 2013

N2 - In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve arbitrary exponential decay rate. Semigroup of linear operators is constructed in analyzing well-posedness and stability of the target systems, and mathematical induction is used in proving existence of kernel functions. An example is also presented, which illustrates performance of the controller. The decay rate estimate derived in this paper is not necessarily equal to decay rate, which can be seen from the appendix.

AB - In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve arbitrary exponential decay rate. Semigroup of linear operators is constructed in analyzing well-posedness and stability of the target systems, and mathematical induction is used in proving existence of kernel functions. An example is also presented, which illustrates performance of the controller. The decay rate estimate derived in this paper is not necessarily equal to decay rate, which can be seen from the appendix.

KW - Antidiffusion

KW - Arbitrary exponential decay rate

KW - Backstepping

KW - Linearized Korteweg-de Vries systems

KW - Semigroup of linear operators

UR - http://www.scopus.com/inward/record.url?scp=84883541821&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84883541821

SN - 9781479901777

T3 - Proceedings of the American Control Conference

SP - 3302

EP - 3307

BT - 2013 American Control Conference, ACC 2013

Y2 - 17 June 2013 through 19 June 2013

ER -