A discontinuous parameter-perturbation method to control chaotic systems

Alexander Jimenez-Triana; Guanrong Chen; John Anzola

doi:10.1109/ACC.2016.7525368

A discontinuous parameter-perturbation method to control chaotic systems

Alexander Jimenez-Triana, Guanrong Chen, John Anzola

Department of Electrical Engineering

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.

Original language	English
Title of host publication	Proceedings of the American Control Conference
Publisher	IEEE
Pages	2954-2958
Volume	2016-July
ISBN (Print)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7525368
Publication status	Published - 28 Jul 2016
Event	2016 American Control Conference (ACC 2016) - Boston, United States Duration: 6 Jul 2016 → 8 Jul 2016 http://acc2016.a2c2.org/index.html

Publication series

Name
Volume	2016-July
ISSN (Print)	0743-1619

Conference

Conference	2016 American Control Conference (ACC 2016)
Country/Territory	United States
City	Boston
Period	6/07/16 → 8/07/16
Internet address	http://acc2016.a2c2.org/index.html

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10.1109/ACC.2016.7525368

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title = "A discontinuous parameter-perturbation method to control chaotic systems",

abstract = "A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.",

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A discontinuous parameter-perturbation method to control chaotic systems. / Jimenez-Triana, Alexander; Chen, Guanrong; Anzola, John.
Proceedings of the American Control Conference. Vol. 2016-July IEEE, 2016. p. 2954-2958.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

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AU - Chen, Guanrong

AU - Anzola, John

PY - 2016/7/28

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N2 - A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.

AB - A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.

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M3 - RGC 32 - Refereed conference paper (with host publication)

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EP - 2958

BT - Proceedings of the American Control Conference

PB - IEEE

T2 - 2016 American Control Conference (ACC 2016)

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A discontinuous parameter-perturbation method to control chaotic systems

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