Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique

The cerebellar model articulation controller (CMAC) is a non-linear adaptive system with built-in simple computation, good generalization capability and fast learning property. In this paper, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive CMAC and H∞ control technique is proposed for a class of chaotic systems with unknown system dynamics and external disturbance. 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 H∞ 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 RIBTC system are derived based on the Lyapunov stability analysis, the Taylor linearization technique and H∞ control theory, so that the stability of the closed-loop system and H∞ tracking performance can be guaranteed. Finally, three application examples, including a Duffing–Holmes chaotic system, a Genesio chaotic system and a Sprott circuit system, are used to demonstrate the effectiveness and performance of proposed robust control technique.