Fuzzy-identification-based adaptive controller design via backstepping approach

This paper proposes a fuzzy-identification-based adaptive control scheme for the chaotic dynamic systems using backstepping control approach, which is referenced as adaptive fuzzy backstepping control (AFBC). The proposed AFBC offers a design approach to drive the chaotic trajectory to track a desired trajectory, and it is comprised of a fuzzy backstepping controller and a robust controller. The fuzzy backstepping controller containing a fuzzy estimation system is the principal controller, and the robust controller is designed to dispel the effect of minimum approximation error introduced by the fuzzy estimation system. Moreover, the Taylor linearization technique is employed to derive the linearized model of the fuzzy estimation system so that all the parameters in the fuzzy system could be updated according. The adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat's lemma, thus the stability of the system can be guaranteed. For comparison, the partial- and full-tuned cases for the parameters in the fuzzy system are simulated. Finally, simulation results verify that the proposed AFBC system can achieve favorable tracking performance for the chaotic system with regard to parameter variations and unknown dynamic function.