Adaptive backstepping control of a class of chaotic systems

This paper deals with the control of a class of chaotic systems using adaptive backstepping, which is a systematic design approach for constructing both feedback control laws and associated Lyapunov functions. First, we show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the so-called non-autonomous “strict-feedback” form. Next, an adaptive backstepping control scheme is extended to the non-autonomous “strict-feedback” system, and it is shown that the output of the non-autonomous system can asymptotically track the output of any known, bounded and smooth nonlinear reference model. Finally, the Duffing oscillator with key constant parameters unknown, is used to illustrated the feasibility of the proposed control scheme. Simulation studies are conducted to show the effectiveness of the proposed method