Adaptive Fuzzy Control for Pure-Feedback Nonlinear Systems With Nonaffine Functions Being Semibounded and Indifferentiable

An adaptive fuzzy control approach is proposed for nonaffine pure-feedback systems with nonaffine functions being semibounded and possibly indifferentiable. A semibounded and continuous condition for nonaffine function is presented to guarantee the controllability of system. To overcome the difficulty from this mild condition, a compact set is introduced, and the nonaffine nonlinear functions are modeled in a new way based on this compact set, which is proved to be invariant set eventually. By using the dynamic surface control (DSC) technique, the problem of explosion of complexity inherent in backstepping method is avoided in the proposed adaptive fuzzy control scheme. Robust compensators are used to minify the influence of uncertainties and disturbances. Furthermore, it is proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.