Controlling chaos in high dimensions

Celso Grebogi; Ying Cheng Lai

doi:10.1109/81.633886

Controlling chaos in high dimensions

Celso Grebogi, Ying Cheng Lai

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

48 Scopus citations

Abstract

We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method, also applicable to high dimensions, is a particular case of the pole placement technique, and we argue that it is the one leading to shortest time to achieve control. Implementation using only a measured time series in experimental situations is described.

Original language	English (US)
Pages (from-to)	971-975
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	44
Issue number	10
DOIs	https://doi.org/10.1109/81.633886
State	Published - 1997
Externally published	Yes

Keywords

Chaos
Control
Pole-placement technique

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/81.633886

Cite this

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title = "Controlling chaos in high dimensions",

abstract = "We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method, also applicable to high dimensions, is a particular case of the pole placement technique, and we argue that it is the one leading to shortest time to achieve control. Implementation using only a measured time series in experimental situations is described.",

keywords = "Chaos, Control, Pole-placement technique",

author = "Celso Grebogi and Lai, {Ying Cheng}",

note = "Funding Information: the University of Kansas, Lawrence. Dr. Lai is the recipient of an NSF Faculty Career Award. Funding Information: Manuscript received April 10, 1997; revised June 10, 1997. This work was supported by the Department of Energy (Mathematical, Information and Computational Sciences Division, High Performance Computing and Communication Program). The work of Y.-C. Lai was supported by AFOSR under Grant F49620-96-1-0066 and by the University of Kansas. This paper was recommended by Guest Editor M. J. Ogorza{\l}ek.",

year = "1997",

doi = "10.1109/81.633886",

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volume = "44",

pages = "971--975",

journal = "IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications",

issn = "1057-7122",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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AU - Lai, Ying Cheng

N1 - Funding Information: the University of Kansas, Lawrence. Dr. Lai is the recipient of an NSF Faculty Career Award. Funding Information: Manuscript received April 10, 1997; revised June 10, 1997. This work was supported by the Department of Energy (Mathematical, Information and Computational Sciences Division, High Performance Computing and Communication Program). The work of Y.-C. Lai was supported by AFOSR under Grant F49620-96-1-0066 and by the University of Kansas. This paper was recommended by Guest Editor M. J. Ogorzałek.

PY - 1997

Y1 - 1997

N2 - We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method, also applicable to high dimensions, is a particular case of the pole placement technique, and we argue that it is the one leading to shortest time to achieve control. Implementation using only a measured time series in experimental situations is described.

AB - We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method, also applicable to high dimensions, is a particular case of the pole placement technique, and we argue that it is the one leading to shortest time to achieve control. Implementation using only a measured time series in experimental situations is described.

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KW - Pole-placement technique

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Controlling chaos in high dimensions

Abstract

Keywords

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