Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements

Wen Kang; Emilia Fridman

doi:10.1109/CDC40024.2019.9029219

Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements

Wen Kang, Emilia Fridman

School of Electrical Engineering

University of Science and Technology Beijing

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

This paper deals with sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain . We suggest to divide the 2D rectangular into N sub-domains, where sensors provide spatially averaged state measurements to be transmitted through communication network. We design a regionally stabilizing controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results.

Original language	English
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	268-273
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9029219
State	Published - Dec 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: 11 Dec 2019 → 13 Dec 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	11/12/19 → 13/12/19

Funding

Funders	Funder number
National Natural Science Foundation of China	61803026
China Postdoctoral Science Foundation	2018M640065, 2019T120047
Israel Science Foundation	1128/14
Fundamental Research Funds for the Central Universities	FRF-TP-18-032A1

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10.1109/CDC40024.2019.9029219

Cite this

Kang, W., & Fridman, E. (2019). Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 268-273). Article 9029219 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029219

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title = "Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements",

abstract = "This paper deals with sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain . We suggest to divide the 2D rectangular into N sub-domains, where sensors provide spatially averaged state measurements to be transmitted through communication network. We design a regionally stabilizing controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results.",

author = "Wen Kang and Emilia Fridman",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

year = "2019",

month = dec,

doi = "10.1109/CDC40024.2019.9029219",

language = "אנגלית",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Kang, W & Fridman, E 2019, Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9029219, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 268-273, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 11/12/19. https://doi.org/10.1109/CDC40024.2019.9029219

Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements. / Kang, Wen; Fridman, Emilia.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 268-273 9029219 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - This paper deals with sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain . We suggest to divide the 2D rectangular into N sub-domains, where sensors provide spatially averaged state measurements to be transmitted through communication network. We design a regionally stabilizing controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results.

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Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements

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