Abstract—Chaos is a very interesting nonlinear phenomenon, and often encountered in many dynamics. Hence, Chaos control problem has been one of the main concerns of researchers wishing to inspect the properties of such systems. This paper focuses on the adaptive control problem and tracking control problem for a new chaotic dynamical system with unknown parameter. Based on a modified backstepping technique and adaptive control method, some chaos controllers are developed for such systems. In comparison with previous methods, the present control technique can improve the speed of parameter identification. The stability analysis in the closed-loop system is given by the Lyapunov method. Finally, numerical simulations are provided to verify the feasibility and effectiveness of the designed controller. 

Index Terms—Chaos control, adaptive control, backstepping, Lyapunov.

Qian Zhang was with the East China University of Science and Technology, shanghai, China. He is now with the Computer Center, East China Normal University, Shanghai, China (e-mail: zq5117@126.com).
Junyi Zhao is with the Computer Center, East China Normal University, Shanghai, China (e-mail: neftwoz@yahoo.com.cn).

Cite:Qian Zhang and Junyi Zhao, "Adaptive Backstepping Control and Tracking Control for New Chaotic Dynamical System," International Journal of Computer and Communication Engineering vol. 2, no. 4, pp. 487-490, 2013.