Compensated-Tracking-Errors-Based Adaptive Fuzzy Controller Design for Uncertain Nonlinear System with Minimal Parameterization

This paper addresses an adaptive fuzzy controller design for a class of nonlinear system. The nonlinear system is in the framework of strict-feedback form. The system funtions are unknown, and external disturbances meet the triangular bound assumption. Takagi-Sugeno (T-S) type fuzzy logic systems are used to approximate the uncertain nonlinear functions. The control objective is to steering the system’s output to track a given signal. The closed-loop control system is proven to be uniformly ultimately bounded, and the tracking error converge to a neighborhood of zero through choosing appropriate parameters. Compensated tracking errors, not tracking errors, are employed to construct the controller, such that the proposed design avoids the repeated differential of virtual control law completely. Furthermore, the adaptive law is in the sense of minimal parameterization. Namely, the number of adaptive law is equal to the order of the nonlinear system. The simulation results show the effectiveness and usage of the proposed strategy.