Development of Adaptive Intelligent Backstepping Tracking Control for Uncertain Chaotic Systems

The cerebellar model articulation controller (CMAC) is a nonlinear adaptive system with built-in simple computation, good generalization capability and fast learning property. In this paper, an adaptive intelligent backstepping tracking control (AIBTC) system combined with adaptive CMAC and
H^∞
control technique is proposed for a class of chaotic systems. In the proposed control system, an adaptive backstepping cerebellar model articulation controller (ABCMAC) is used to mimic an ideal backstepping control (IBC), and a robust controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. Moreover, the all adaptation laws of the AIBTC system are derived based on the Lyapunov stability analysis and
H^∞
control theory, so that the stability of the closed-loop system can be guaranteed. Finally, two application examples are used to demonstrate the effectiveness of proposed control technique.