Sampled-data delayed feedback control for stabilizing unstable periodic orbits

Ahmet Cetinkaya; Tomohisa Hayakawa

doi:10.1109/CDC.2015.7402408

Sampled-data delayed feedback control for stabilizing unstable periodic orbits

Ahmet Cetinkaya, Tomohisa Hayakawa

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

2 Citations (Scopus)

Abstract

A sampled-data delayed feedback control framework is proposed for stabilizing both periodic solutions of linear periodic systems and unstable periodic orbits of nonlinear systems. The proposed control framework utilizes the difference between two consecutive samples of the state as a feedback input. The controller is turned on and off periodically in an alternating fashion, allowing us to obtain a monodromy matrix for the closed-loop system under our proposed control law. We investigate asymptotic behavior of the closed-loop system state trajectories through an analysis of the obtained monodromy matrix. Finally, we present a numerical example to demonstrate the efficacy of our approach.

Original language	English
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1409-1414
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7402408
Publication status	Published - 2015 Feb 8
Externally published	Yes
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: 2015 Dec 15 → 2015 Dec 18

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country/Territory	Japan
City	Osaka
Period	15/12/15 → 15/12/18

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2015.7402408

Cite this

Cetinkaya, A., & Hayakawa, T. (2015). Sampled-data delayed feedback control for stabilizing unstable periodic orbits. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 1409-1414). [7402408] (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402408

Sampled-data delayed feedback control for stabilizing unstable periodic orbits. / Cetinkaya, Ahmet; Hayakawa, Tomohisa.
54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1409-1414 7402408 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

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

Cetinkaya, A & Hayakawa, T 2015, Sampled-data delayed feedback control for stabilizing unstable periodic orbits. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7402408, Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 1409-1414, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 15/12/15. https://doi.org/10.1109/CDC.2015.7402408

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AB - A sampled-data delayed feedback control framework is proposed for stabilizing both periodic solutions of linear periodic systems and unstable periodic orbits of nonlinear systems. The proposed control framework utilizes the difference between two consecutive samples of the state as a feedback input. The controller is turned on and off periodically in an alternating fashion, allowing us to obtain a monodromy matrix for the closed-loop system under our proposed control law. We investigate asymptotic behavior of the closed-loop system state trajectories through an analysis of the obtained monodromy matrix. Finally, we present a numerical example to demonstrate the efficacy of our approach.

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Sampled-data delayed feedback control for stabilizing unstable periodic orbits

Abstract

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ASJC Scopus subject areas

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