Observer‐based controller design for uncertain disturbed Takagi‐Sugeno fuzzy systems: A fuzzy wavelet neural network approach

Abstract

SummaryIn this article, we develop a novel method to design a controller for nonlinear systems represented by Takagi‐Sugeno (T‐S) fuzzy model in the presence of unknown dynamics, uncertainties in parameters of nonlinear system and external disturbances. The control law is constituted two segments. The first segment derives from parallel distributed compensation (PDC) procedure, in which each control rule is drawn from the respective rule of T‐S fuzzy model. The second segment stems from fuzzy wavelet neural network (FWNN) estimator which is evoked by the hypothesis of multiresolution analysis (MRA) of wavelet transforms and fuzzy notions, so as to approximate the uncertainties and external disturbances in T‐S fuzzy model accurately. In this regard, the Lyapunov stability theorem is applied to acquire the adaptive learning laws for training and tuning online FWNN parameters such as the dilations, translations, and the weights of networks. Moreover, the asymptotic stability of the closed loop system is guaranteed based on the Lyapunov stability theorem. Furthermore, a development of the proposed method to observer‐based controller design for uncertain nonlinear systems descripted by T‐S fuzzy model is provided. The efficiency and robustness of the proposed method are illustrated by simulation outcomes. It is noteworthy that the proposed controller remarkably handles the uncertainties and external disturbances in T‐S fuzzy model without employing traditional conservative lemma and without considering bounds on uncertainties.