Discrete Dynamics in Nature and Society 
Volume 4 (2000), Issue 4, Pages 257-267
doi:10.1155/S1026022600000248

Nonlinear control of chaotic systems:A switching manifold approach

Jin-Qing Fang,1 Yiguang Hong,2 Huashu Qin,2 and Guanrong Chen3

 1China Institute of Atomic Energy, P.O. Box 275-27, Beijing 102413, China
2lnstitute of Systems Science, Academia Sinica, Beijing 100080, China
3Department of Electrical and Computer Engineering, University of Houston, Houston 77204-4793, TX, USA
Received 20 November 1998

Abstract

In this paper, a switching manifold approach is developed for nonlinear feed-back control of chaotic systems. The design strategy is straightforward, and the nonlinear control law is the simple bang–bang control. Yet, this control method is very effective; for instance, several desired equilibria can be stabilized by using one control law with different initial conditions. Its effectiveness is verified by both theoretical analysis and numerical simulations. The Lorenz system simulation is shown for the purpose of illustration.