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

30 Scopus citations

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

Funding

Funders	Funder number
Beijing Science Foundation for the Excellent Youth Scholars	2018000020124G067
Outstanding Chinese and Foreign Youth Exchange Program of China Association of Science and Technology
National Natural Science Foundation of China	61803026
Israel Science Foundation	1128/14
Centre National de la Recherche Scientifique
Ministry of Science and Technology, Israel
Fundamental Research Funds for the Central Universities	FRF-TP-18-032A1

Keywords

Event-trigger
Korteweg–de Vries equation
LMIs

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10.1016/j.automatica.2020.109315

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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.",

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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.

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

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