Control and applications of chaos

Celso Grebogi, Ying-Cheng Lai, Scott Hayes

Research output: Contribution to journalArticle

21 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 event such as the voltage collapse.

Original languageEnglish (US)
Pages (from-to)1115-1146
Number of pages32
JournalJournal of the Franklin Institute
Volume334
Issue number5-6
StatePublished - Sep 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

  • Modeling and Simulation
  • Control and Optimization
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Information Systems and Management
  • Signal Processing

Cite this

Grebogi, C., Lai, Y-C., & Hayes, S. (1997). Control and applications of chaos. Journal of the Franklin Institute, 334(5-6), 1115-1146.

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

In: Journal of the Franklin Institute, Vol. 334, No. 5-6, 09.1997, p. 1115-1146.

Research output: Contribution to journalArticle

Grebogi, C, Lai, Y-C & Hayes, S 1997, 'Control and applications of chaos', Journal of the Franklin Institute, vol. 334, no. 5-6, pp. 1115-1146.
Grebogi C, Lai Y-C, Hayes S. Control and applications of chaos. Journal of the Franklin Institute. 1997 Sep;334(5-6):1115-1146.
Grebogi, Celso ; Lai, Ying-Cheng ; Hayes, Scott. / Control and applications of chaos. In: Journal of the Franklin Institute. 1997 ; Vol. 334, No. 5-6. pp. 1115-1146.
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