Finite-time boundary stabilization for Korteweg–de Vries–Burgers equations

Shuang Liang; Kai Ning Wu; Ming Xin He

doi:10.1016/j.cnsns.2022.106836

Finite-time boundary stabilization for Korteweg–de Vries–Burgers equations

Shuang Liang
, Kai Ning Wu^*
, Ming Xin He

^*Corresponding author for this work

Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The finite-time boundary stabilization is investigated for Korteweg–de Vries–Burgers (KdVB) equations. Firstly, a distributed controller is derived, and criteria are presented to guarantee the finite-time stability (FTS) of KdVB equations via the distributed controller. Then, considering the installation in real applications, a vogue control strategy, a boundary controller design, is adopted to ensure the FTS. In light of the FTS lemma, sufficient conditions are obtained for KdVB equations to ensure the FTS. When there exist uncertainties in the system's coefficients, the robust finite-time stabilization is studied for uncertain KdVB equations. With the designed boundary controller, a sufficient condition is provided to ensure the FTS for the uncertain KdVB equation. Finally, the theoretical results are verified by numerical examples.

Original language	English
Article number	106836
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	116
DOIs	https://doi.org/10.1016/j.cnsns.2022.106836
State	Published - Jan 2023
Externally published	Yes

Keywords

Boundary control
Finite-time stability
Korteweg–de Vries–Burgers equations
Robust stabilization

Access to Document

10.1016/j.cnsns.2022.106836

Cite this

@article{a1df346826e6439082b1d64974f51286,

title = "Finite-time boundary stabilization for Korteweg–de Vries–Burgers equations",

abstract = "The finite-time boundary stabilization is investigated for Korteweg–de Vries–Burgers (KdVB) equations. Firstly, a distributed controller is derived, and criteria are presented to guarantee the finite-time stability (FTS) of KdVB equations via the distributed controller. Then, considering the installation in real applications, a vogue control strategy, a boundary controller design, is adopted to ensure the FTS. In light of the FTS lemma, sufficient conditions are obtained for KdVB equations to ensure the FTS. When there exist uncertainties in the system's coefficients, the robust finite-time stabilization is studied for uncertain KdVB equations. With the designed boundary controller, a sufficient condition is provided to ensure the FTS for the uncertain KdVB equation. Finally, the theoretical results are verified by numerical examples.",

keywords = "Boundary control, Finite-time stability, Korteweg–de Vries–Burgers equations, Robust stabilization",

author = "Shuang Liang and Wu, \{Kai Ning\} and He, \{Ming Xin\}",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

month = jan,

doi = "10.1016/j.cnsns.2022.106836",

language = "英语",

volume = "116",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Finite-time boundary stabilization for Korteweg–de Vries–Burgers equations

AU - Liang, Shuang

AU - Wu, Kai Ning

AU - He, Ming Xin

PY - 2023/1

Y1 - 2023/1

N2 - The finite-time boundary stabilization is investigated for Korteweg–de Vries–Burgers (KdVB) equations. Firstly, a distributed controller is derived, and criteria are presented to guarantee the finite-time stability (FTS) of KdVB equations via the distributed controller. Then, considering the installation in real applications, a vogue control strategy, a boundary controller design, is adopted to ensure the FTS. In light of the FTS lemma, sufficient conditions are obtained for KdVB equations to ensure the FTS. When there exist uncertainties in the system's coefficients, the robust finite-time stabilization is studied for uncertain KdVB equations. With the designed boundary controller, a sufficient condition is provided to ensure the FTS for the uncertain KdVB equation. Finally, the theoretical results are verified by numerical examples.

AB - The finite-time boundary stabilization is investigated for Korteweg–de Vries–Burgers (KdVB) equations. Firstly, a distributed controller is derived, and criteria are presented to guarantee the finite-time stability (FTS) of KdVB equations via the distributed controller. Then, considering the installation in real applications, a vogue control strategy, a boundary controller design, is adopted to ensure the FTS. In light of the FTS lemma, sufficient conditions are obtained for KdVB equations to ensure the FTS. When there exist uncertainties in the system's coefficients, the robust finite-time stabilization is studied for uncertain KdVB equations. With the designed boundary controller, a sufficient condition is provided to ensure the FTS for the uncertain KdVB equation. Finally, the theoretical results are verified by numerical examples.

KW - Boundary control

KW - Finite-time stability

KW - Korteweg–de Vries–Burgers equations

KW - Robust stabilization

UR - https://www.scopus.com/pages/publications/85137719595

U2 - 10.1016/j.cnsns.2022.106836

DO - 10.1016/j.cnsns.2022.106836

M3 - 文章

AN - SCOPUS:85137719595

SN - 1007-5704

VL - 116

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 106836

ER -

Finite-time boundary stabilization for Korteweg–de Vries–Burgers equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this