Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition

Rami Katz; Emilia Fridman

doi:10.1109/LCSYS.2021.3133492

Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition

Rami Katz, Emilia Fridman

School of Electrical Engineering

Tel Aviv University

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

Abstract

In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.

Original language	English
Pages (from-to)	1814-1819
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	6
DOIs	https://doi.org/10.1109/LCSYS.2021.3133492
State	Published - 2022

Keywords

Distributed parameter systems
boundary control
nonlinear parabolic PDEs

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Control and Optimization

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10.1109/LCSYS.2021.3133492

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title = "Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition",

abstract = "In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.",

keywords = "Distributed parameter systems, boundary control, nonlinear parabolic PDEs",

author = "Rami Katz and Emilia Fridman",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2022",

doi = "10.1109/LCSYS.2021.3133492",

language = "الإنجليزيّة",

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T1 - Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition

AU - Katz, Rami

AU - Fridman, Emilia

PY - 2022

Y1 - 2022

N2 - In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.

AB - In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.

KW - Distributed parameter systems

KW - boundary control

KW - nonlinear parabolic PDEs

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U2 - 10.1109/LCSYS.2021.3133492

DO - 10.1109/LCSYS.2021.3133492

M3 - مقالة

SN - 2475-1456

VL - 6

SP - 1814

EP - 1819

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -

Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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