Event-triggered control of Korteweg–de Vries equation under averaged measurements

Wen Kang; Lucie Baudouin; Emilia Fridman

doi:10.1016/j.automatica.2020.109315

Event-triggered control of Korteweg–de Vries equation under averaged measurements

Wen Kang^*, Lucie Baudouin, Emilia Fridman

^*Corresponding author for this work

School of Electrical Engineering

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

Abstract

This work addresses distributed event-triggered control law of 1-D nonlinear Korteweg–de Vries (KdV) equation posed on a bounded domain. Such a system, in a continuous framework, is exponentially stabilizable by a linear state feedback as a source term. Here we consider the situation where the feedback is sampled in time and piecewise averaged in space, and an event-triggering mechanism is designed to maintain stability of this infinite dimensional system. Both well-posedness of the closed-loop system and avoiding the Zeno behaviour issues are addressed. Sufficient LMI-based conditions are constructed to guarantee the regional exponential stability. Numerical examples illustrate the efficiency of the method.

Original language	English
Article number	109315
Journal	Automatica
Volume	123
DOIs	https://doi.org/10.1016/j.automatica.2020.109315
State	Published - Jan 2021

Keywords

Event-trigger
Korteweg–de Vries equation
LMIs

Access to Document

10.1016/j.automatica.2020.109315

Cite this

@article{96b15010fb654706a9ac6be1b315d69e,

title = "Event-triggered control of Korteweg–de Vries equation under averaged measurements",

abstract = "This work addresses distributed event-triggered control law of 1-D nonlinear Korteweg–de Vries (KdV) equation posed on a bounded domain. Such a system, in a continuous framework, is exponentially stabilizable by a linear state feedback as a source term. Here we consider the situation where the feedback is sampled in time and piecewise averaged in space, and an event-triggering mechanism is designed to maintain stability of this infinite dimensional system. Both well-posedness of the closed-loop system and avoiding the Zeno behaviour issues are addressed. Sufficient LMI-based conditions are constructed to guarantee the regional exponential stability. Numerical examples illustrate the efficiency of the method.",

keywords = "Event-trigger, Korteweg–de Vries equation, LMIs",

author = "Wen Kang and Lucie Baudouin and Emilia Fridman",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2021",

month = jan,

doi = "10.1016/j.automatica.2020.109315",

language = "אנגלית",

volume = "123",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - Event-triggered control of Korteweg–de Vries equation under averaged measurements

AU - Kang, Wen

AU - Baudouin, Lucie

AU - Fridman, Emilia

PY - 2021/1

Y1 - 2021/1

N2 - This work addresses distributed event-triggered control law of 1-D nonlinear Korteweg–de Vries (KdV) equation posed on a bounded domain. Such a system, in a continuous framework, is exponentially stabilizable by a linear state feedback as a source term. Here we consider the situation where the feedback is sampled in time and piecewise averaged in space, and an event-triggering mechanism is designed to maintain stability of this infinite dimensional system. Both well-posedness of the closed-loop system and avoiding the Zeno behaviour issues are addressed. Sufficient LMI-based conditions are constructed to guarantee the regional exponential stability. Numerical examples illustrate the efficiency of the method.

AB - This work addresses distributed event-triggered control law of 1-D nonlinear Korteweg–de Vries (KdV) equation posed on a bounded domain. Such a system, in a continuous framework, is exponentially stabilizable by a linear state feedback as a source term. Here we consider the situation where the feedback is sampled in time and piecewise averaged in space, and an event-triggering mechanism is designed to maintain stability of this infinite dimensional system. Both well-posedness of the closed-loop system and avoiding the Zeno behaviour issues are addressed. Sufficient LMI-based conditions are constructed to guarantee the regional exponential stability. Numerical examples illustrate the efficiency of the method.

KW - Event-trigger

KW - Korteweg–de Vries equation

KW - LMIs

UR - http://www.scopus.com/inward/record.url?scp=85094864168&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2020.109315

DO - 10.1016/j.automatica.2020.109315

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85094864168

SN - 0005-1098

VL - 123

JO - Automatica

JF - Automatica

M1 - 109315

ER -

Event-triggered control of Korteweg–de Vries equation under averaged measurements

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this