Indirect Adaptive Fuzzy Control for Nonaffine Nonlinear Pure-Feedback Systems

In this article, an indirect adaptive fuzzy control scheme is proposed for single-input, single-output (SISO) nonaffine nonlinear systems in a pure-feedback form. In this scheme, the unknown nonlinear functions are approximated by Takagi-Sugeno (T-S) fuzzy logic systems with an state observer. The adaptive laws are developed to adjust the parameters of the fuzzy systems. The stability of the closed-loop system is proved with all state variables being uniformly bounded in the Lyapunov sense and the tracking error is confirmed to zero asymptotically. Finally, simulation results obtained for two practical examples show the feasibility and effectiveness of the proposed scheme.