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.

FWNNet: Presentation of a New Classifier of Brain Tumor Diagnosis Based on Fuzzy Logic and the Wavelet‐Based Neural Network Using Machine‐Learning Methods

“…In the T-S fuzzy model, it is accurate to predict uncertainties and external disturbances. The T-S fuzzy models suggested approach for observer-based controller design for uncertain nonlinear systems has been improved [ 24 ]. Zirkohi and Shoja-Majidabad [ 25 ] suggested an efficient adaptive control technique to explore synchronizing two chaotic systems.…”

“…Consequently, the number of iterations required to train the FWNN structure is reduced, and function approximation precision is improved over NNs [ 24 ]. In this paper, the presented classifier is implemented in the brain tumor diagnosis.…”

Adaptive fuzzy output feedback fault‐tolerant control of switched nonlinear systems with sensor and actuator faults

“…[12][13][14][15][16] In addition, fuzzy logic systems (FLSs) and neural networks (NNs), as universal function approximators, [17][18][19][20][21] can be employed to approximate the unknown nonlinearities, 22 some adaptive fuzzy or NNs control methods have been gradually presented for nonlinear systems. [23][24][25] Subsequently, many important results for switched nonlinear systems have been developed successfully. The authors in Reference 26 studied a class of uncertain nonlinear switched systems and improved the classical average dwell time (ADT) method.…”

Event‐triggered integral sliding mode control of Takagi‐Sugeno fuzzy stochastic systems

“…In problems, where all the state vectors are not completely measurable, the controller has to be combined with a state observer to determine the state vector. Therefore, the new developments of the observer‐based control schemes designed for a particular class of dynamical systems have attracted more attraction in the recent decades 6‐8 . However, several realistic problems are shown in the pattern of nonlinear stochastic systems which can be represented by the type of It stochastic differential equations, for example, mechanical systems, economic systems and biological systems, and so on.…”