A Hybrid Learning Algorithm for Fuzzy Wavelet Networks Design for Functions Approximation, Online Identification and Control of Nonlinear Systems

In this paper, a hybrid learning algorithm is presented for fuzzy wavelet networks (FWNs) design for functions approximation, online identification and control of nonlinear systems. The proposed algorithm is based on orthogonal least square (OLS) algorithm, Shufled Frog Leaping (SFL) algorithm and recursive least square method (RLS). The OLS algorithm is used for determine network dimensions, number of fuzzy rules and wavelets in each fuzzy rule and for purifying wavelets in each sub-WNN. So, after selection of important wavelets based on training data set, FWN structure is constructed and initial values of the network parameters are determined. Then linear and nonlinear parameters of the network are tuned based on recursive least square method and SFL algorithm, respectively. In order to show the capabilities and effectiveness of the proposed method, simulation results are presented for some example: function approximation, online identification and control of nonlinear systems. Also, the results obtained by the proposed approach are compared with the previous approaches reported in the literature. Simulation results show that the proposed method improves model approximation accuracy and performance index by using less number of fuzzy rules compare to other methods for study systems.