A Wavelet-Based Robust Adaptive T-S Fuzzy Controller Design for Synchronization of Faulty Chaotic Gyrostat Systems

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.

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