A simple adaptive fuzzy control for a class of strict-feedback SISO systems

A simple adaptive fuzzy control (SAFC) is proposed for a class of strict-feedback uncertain nonlinear systems with both unknown system nonlinearities and unknown virtual control gain nonlinearities. Combining the dynamic surface control (DSC) technique with minimal-learning-parameters (MLP) algorithm, a systematic procedure for synthesis of SAFC is developed base on the universal approximation of Takagi-Sugeno (T-S) fuzzy system. An important feature of the proposed algorithm is that the number of parameters updated on line for each subsystem is reduced dramatically to one, both problems of ldquoexplosion of complexityrdquo and ldquocurse of dimensionrdquo are avoided, such that the computation load is reduced drastically. It is shown that all closed-loop signals are semi-global uniform ultimate bound (SGUUB) via Lyapunov stability theory and the tracking error can be made arbitrary small. Finally, simulation results are presented to demonstrate the effectiveness and performance of the proposed scheme.