Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 439324, 20 pages
http://dx.doi.org/10.1155/2011/439324
Research Article

New Nonlinear Controller for a Class of Chaotic Systems Based on Adaptive Backstepping Fuzzy-Immune Control

Kai-Shiuan Shih,1 Tzuu-Hseng S. Li,1 and Shun-Hung Tsai2

1aiRobots Laboratory, Department of Electrical Engineering, National Cheng Kung University, Tainan 70101, Taiwan
2Graduate Institute of Automation Technology, National Taipei University of Technology, Taipei 10608, Taiwan

Received 31 July 2010; Revised 15 March 2011; Accepted 28 March 2011

Academic Editor: E. E. N. Macau

Copyright © 2011 Kai-Shiuan Shih et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An adaptive backstepping fuzzy-immune controller for a class of chaotic systems is proposed. An adaptive backstepping fuzzy method and adaptive laws are used to approximate nonlinear functions and the unknown upper bounds of uncertainty, respectively. The proposed adaptive backstepping fuzzy-immune controller guarantees the stability of a class of chaotic systems while maintaining good tracking performance. The fuzzy-immune algorithm is used for mathematical calculations. The intelligence algorithm consists of the adaptive backstepping fuzzy method and a novel fuzzy-immune scheme which generates optimal parameters for the control schemes. Finally, two simulation examples are given to illustrate the effectiveness of the proposed approach.