Fuzzy Wavelet Neural Network Models for Prediction and Identification of Dynamical Systems

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Abstract
This paper presents fuzzy wavelet neural network (FWNN) models for prediction and identification of nonlinear dynamical systems. The proposed FWNN models are obtained from the traditional Takagi-Sugeno-Kang fuzzy system by replacing the THEN part of fuzzy rules with wavelet basis functions that have the ability to localize both in time and frequency domains. The first and last model use summation and multiplication of dilated and translated versions of single-dimensional wavelet basis functions, respectively, and in the second model, THEN parts of the rules consist of radial function of wavelets. Gaussian type of activation functions are used in IF part of the fuzzy rules. A fast gradient-based training algorithm, i.e., the Broyden-Fletcher-Goldfarb-Shanno method, is used to find the optimal values for unknown parameters of the FWNN models. Simulation examples are also given to compare the effectiveness of the models with the other known methods in the literature. According to simulation results, we see that the proposed FWNN models have impressive generalization ability.

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