Adaptive output control of a class of uncertain chaotic systems

In this paper, a new observer-based backstepping output control scheme is proposed for stabilizing and controlling a class of uncertain chaotic systems. The controller is designed through the use of a robust observer and backstepping technique. We firstly show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the feedback form. Secondly, the synchronization problem is converted to the tracking problem from control theory, thereby leading to the use of state observer design techniques. A new observer is utilized to estimate the unmeasured states. Unlike some existing methods for chaos control, no priori knowledge on the system parameters is required and only the output signal is available for control purpose. The Lyapunov functions are quadratic in the state estimates, the observer errors and the parameter estimation error based on the backstepping technique. It is shown that not only global stability is guaranteed by the proposed controller, but also both transient and asymptotic tracking performances are quantified as explicit functions of the design parameters so that designers can tune the design parameters in an explicit way to obtain the desired closed-loop behavior.