A Wavelet-Based Robust Adaptive T-S Fuzzy Controller Design for Synchronization of Faulty Chaotic Gyrostat Systems
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A Wavelet-Based Robust Adaptive T-S Fuzzy Controller Design for Synchronization of Faulty Chaotic Gyrostat Systems Yousef Farid1 · Amin Ramezani1 Received: 7 November 2019 / Revised: 19 July 2020 / Accepted: 8 September 2020 © Brazilian Society for Automatics--SBA 2020
Abstract In this study, the synchronization problem of the faulty chaotic gyrostat master–slave systems using a wavelet-based robust adaptive T-S fuzzy control is investigated. This control system is comprised of a wavelet T-S fuzzy network (TSFN) controller, a feedback controller and a robust controller. Within this scheme, the wavelet TSFN is used in two separate approaches. At the first approach, it is utilized to approximate the nonlinear functions of the gyrostat systems, and at the second approach, it is used to approximate the lumped fault function of the control system. The feedback controller is developed to initially control the underlying system, and a robust controller is an adaptive controller which is used to dispel the effects of the approximation errors on the tracking performance. The parameters of wavelet TSFN and the bound parameter of the robust controller are tuned on-line by the derived adaptive laws based on Lyapunov stability analysis. The wavelet block acts as a feature extractor, reduces the number of fuzzy rules and also acts as a normalization block. The Lyapunov stability of the closed-loop system, robustness against the parameters uncertainties, the external disturbances and the approximation errors, as well as the convergence of the tracking errors and boundedness of all signals in the closed-loop system, are guaranteed. Finally, the synchronization problem of the unknown chaotic gyrostat systems in the presence of parameter uncertainties, external disturbances and actuator faults is simulated to illustrate the effectiveness of the proposed control scheme. Keywords Gyrostat systems · Chaos synchronization · Fault-tolerant control · Wavelet TSFN · Adaptive control
1 Introduction A chaotic system is a nonlinear deterministic system exhibiting complex and unpredictable behavior. In the past three decades, many engineering applications of chaotic systems have been studied including secure communication, digital communication, power electronic devices, biological systems, chemical reaction analysis and information processing (Chen et al. 2020; Bigdeli and Farid 2012; Farid and Bigdeli 2013; Yadav et al. 2019; Aghababa 2018; Farid and Moghaddam 2014). The main special attribute of a chaotic system is that a tiny change in its initial conditions and parameters leads to an enormous difference in the long-term behavior of the system. The synchronization problem of a dynamical system is one of the classic topics in engineering science. Synchro-
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Amin Ramezani [email protected] http://www.modares.ac.ir/~ramezani School of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran
nization problem of the chaotic systems has attracted much attention since the work of Pecora and Car
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