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Direct Adaptive Fuzzy Control for a Class of Nonlinear Systems Based on Integral Lyapunov Functions

In this paper, a direct adaptive fuzzy control scheme is developed for a class of uncertain nonlinear systems based on integral Lyapunov functions. In this scheme, using the fuzzy logic system online approximation capability, the fuzzy approximator is used to design a direct adaptive fuzzy controller, and the unknown parameters are adjusted by the time-varying dead-zone, which its size is adjusted adaptively. The proposed design scheme guarantees that all the signals in the resulting closed-loop system are bounded, and the tracking error converges to a small neighborhood of the origin. Finally, a simulation example is used to demonstrate the effectiveness of the proposed control scheme.