Finite-dimensional control of the Kuramoto-Sivashinsky equation under point measurement and actuation

Rami Katz, Emilia Fridman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations

Abstract

Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the 1D heat equation, under assumption that at least one of the observation or control operators is bounded. This paper suggests a constructive method for such controllers in the case where both the observation and control operators are unbounded. We consider boundary control of the 1D linear Kuramoto-Sivashinsky equation with in-domain point measurement. We employ a modal decomposition approach via dynamic extension, where we use the eigenfunctions of a Sturm-Liouville operator. The controller dimension is defined by the number of unstable modes, whereas the observer's dimension N may be larger than this number. We suggest a direct Lyapunov approach to the full-order closedloop system and provide LMIs for finding N and the resulting exponential decay rate. We prove that the LMIs are always feasible, provided N is large enough. A numerical example demonstrates the efficiency of the method and shows that the resulting LMIs are non-conservative.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4423-4428
Number of pages6
ISBN (Electronic)9781728174471
DOIs
StatePublished - 14 Dec 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: 14 Dec 202018 Dec 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island
Period14/12/2018/12/20

Funding

FundersFunder number
Israel Science Foundation673/19
Israel Science Foundation
Tel Aviv University

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