Controlling chaos in high dimensions

Author

Grebogi, Celso ; Lai, Ying-Cheng

Author_Institution

Inst. fur Theor. Phys. und Astrophys., Potsdam Univ., Germany

Volume

44

Issue

10

fYear

1997

fDate

10/1/1997 12:00:00 AM

Firstpage

971

Lastpage

975

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 theory; delays; discrete time systems; feedback; nonlinear dynamical systems; pole assignment; stability; system theory; Ott-Grebogi-Yorke method; chaos control; chaotic attractor; feedback control; high dimensions; higher dimensional dynamics; pole placement technique; stabilization; time periodic motion; time series; unstable periodic orbits; Chaos; Chaotic communication; Control systems; Extraterrestrial measurements; Feedback control; High performance computing; Motion control; Orbits; State feedback; Time measurement;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.633886

Filename

633886