Control and applications of chaos

Celso Grebogi, Ying-Cheng Lai, Scott Hayes

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

This review describes a procedure for stabilizing a desirable chaotic orbit embedded in a chaotic attractor of dissipative dynamical systems by using small feedback control. The key observation is that certain chaotic orbits may correspond to a desirable system performance. By carefully selecting such an orbit, and then applying small feedback control to stabilize a trajectory from a random initial condition around the target chaotic orbit, desirable system performance can be achieved. As applications, three examples are considered: (1) synchronization of chaotic systems; (2) conversion of transient chaos into sustained chaos; and (3) controlling symbolic dynamics for communication. The first and third problems are potentially relevant to communication in engineering, and the solution of the second problem can be applied to electrical power systems to avoid catastrophic events such as the voltage collapse.

Original languageEnglish (US)
Pages (from-to)2175-2197
Number of pages23
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume7
Issue number10
StatePublished - Oct 1997
Externally publishedYes

Fingerprint

Chaos theory
Chaos
Orbits
Orbit
Feedback Control
Feedback control
System Performance
Dissipative Dynamical System
Symbolic Dynamics
Chaotic systems
Communication
Chaotic Attractor
Power System
Chaotic System
Synchronization
Dynamical systems
Initial conditions
Voltage
Trajectories
Trajectory

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

Control and applications of chaos. / Grebogi, Celso; Lai, Ying-Cheng; Hayes, Scott.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 7, No. 10, 10.1997, p. 2175-2197.

Research output: Contribution to journalArticle

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