Abstract
Fuzzy neural networks, with suitable learning strategy, have been demonstrated as an effective tool for online data modeling. However, it is a challenging task to construct a model to ensure its quality and stability for non-stationary dynamic systems with some uncertainties. To solve this problem, this paper presents a novel identification model based on recurrent interval type-2 fuzzy wavelet neural network (RIT2FWNN) with new learning algorithm. The model benefits from both advantages of recurrent and wavelet neural networks such as use of temporal data and fast convergence properties. The proposed antecedent and consequent parameters update rules are derived using sliding-mode-control-theory. To evaluate the proposed fuzzy model, it is utilized to design a nonlinear model-based predictive controller and is applied for the synchronization of fractional-order time-delay chaotic systems. Using Lyapunov stability analysis, it is shown that all update rules of the parameters are uniformly ultimately bounded. The adaptation laws obtained in this method are very simple and have closed forms. Some stability conditions are derived to prove learning dynamics and asymptotic stability of the network by using an appropriate Lyapunov function. The efficacy and performance of the proposed method is verified by simulation examples.
Highlights
In the study of nonlinear dynamical system identification, conventional modeling approaches may not be suitable to be used due to the lack of precise, formal knowledge about the system, strongly nonlinear behavior, a high degree of uncertainty and time-varying characteristics
Since the output of dynamic systems is a function of time-delayed input and time-delayed output, recurrent neural network (RNN) is suitable choice for identifying their behaviour
Lin and Lee developed an adaptive fuzzy-control scheme incorporating with Sliding mode control (SMC) approach to synchronize two nonlinear fractional-order Duffing-Holmes chaotic systems [16]
Summary
In the study of nonlinear dynamical system identification, conventional modeling approaches may not be suitable to be used due to the lack of precise, formal knowledge about the system, strongly nonlinear behavior, a high degree of uncertainty and time-varying characteristics. In [4], a direct adaptive fuzzy controller is designed to obtain a generalized projective synchronization of two different incommensurate fractional-order chaotic systems in the presence of both uncertain dynamics and external disturbances. Lin and Lee developed an adaptive fuzzy-control scheme incorporating with SMC approach to synchronize two nonlinear fractional-order Duffing-Holmes chaotic systems [16] They investigated the effect of delay on the chaotic behavior of the fractionalorder system for the first time. The models of real-world systems is not known completely and/or their accuracy are affected by nonlinear and time-varying behaviour which can be originated from actual high degrees of uncertainties about the plant or from the plant dynamics, external disturbances and time-varying parameters
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