Indirect‐Approximator‐Based Adaptive Tracking Control for Uncertain Nonlinear Systems

ABSTRACT

This paper addresses the adaptive tracking control problem for a class of uncertain nonlinear systems. Conventional approximation‐based control methods usually employ fuzzy logic systems (FLSs) or neural networks to directly approximate unknown nonlinear functions. However, the resulting approximation error is highly dependent on the selection of basis‐function parameters, which are often empirically chosen and difficult to characterize precisely. This limitation may degrade the approximation capability and consequently affect the tracking performance. To overcome this issue, the states of the original system are augmented, and a fuzzy state observer is developed to construct an indirect fuzzy approximator for the unknown nonlinear functions. In the proposed framework, the approximation error is equivalently represented by the fuzzy observation error, which can be explicitly regulated through the observer gains. Based on the proposed indirect fuzzy approximator and an adaptive design strategy, an indirect‐approximator‐based adaptive tracking controller is developed. Compared with traditional direct approximation‐based methods, the proposed controller can achieve improved tracking performance by driving the tracking error into a smaller residual set. The stability of the closed‐loop system and the convergence property of the tracking error are rigorously analysed. Finally, simulation and experimental results are provided to demonstrate the effectiveness and superiority of the proposed method.