Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 347210, 12 pages
http://dx.doi.org/10.1155/2012/347210
Research Article

Adaptive Feedback Control for Chaos Control and Synchronization for New Chaotic Dynamical System

M. M. El-Dessoky1,2 and M. T. Yassen2

1Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 8 February 2012; Revised 23 April 2012; Accepted 2 May 2012

Academic Editor: Rafael Martinez-Guerra

Copyright © 2012 M. M. El-Dessoky and M. T. Yassen. 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

This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov's stability theory, adaptive control law is derived such that the trajectory of the new system with unknown parameters is globally stabilized to the origin. In addition, an adaptive control approach is proposed to make the states of two identical systems with unknown parameters asymptotically synchronized. Numerical simulations are shown to verify the analytical results.