Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

Abstract

The output regulation problem for pure-feedback non-linear systems with prescribed performance (PP) driven by an external linear system with unknown parameter are investigated. First, an observer with a disturbance signal is designed to observe unmeasured system states. Secondly, fuzzy logic systems (FLS) are used to approximate unknown non-linear non-affine functions. Thirdly, a fuzzy internal model is obtained to reject disturbance, and an adaptive fuzzy output feedback algorithm is proposed based on dynamic surface control (DSC) technique and backstepping method. Simultaneously, an L function is constructed so that the overall property (steady-state property and dynamic property) of the tracking error are constrained by PP functions. The results explain that the proposed control algorithm can make sure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the tracking error is semi-globally PP uniformly ultimately bounded (SPPUUB). Finally, two examples are given to show the validity of the results.