Nonlinear System Modeling and Control with Dynamic Fuzzy Wavelet Neural Network

Abstract

This paper proposes a fuzzy neural network model which is dynamic and uses wavelet functions in its processing units. Because of that this new model is called as dynamic fuzzy wavelet neural network (DFWNN). In the DFWNN model, IF part of the fuzzy rules are comprised of Mexican Hat wavelet membership functions and THEN part of the rules are differential equations of linear functions. For nonlinear system modeling and/or control applications, in order to find optimal model parameters, a gradient based algorithm Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used. Gradients in this algorithm is calculated by using adjoint sensitivity method. To show the modeling and the control performance of the proposed model, a highly nonlinear and a well-known chemical process continuously stirred tank reactor system (CSTR) is selected. From the simulation results, it can be seen that the DFWNN model demonstrated both high approximation accuracy, and at the same time, good generalization performance in modeling of internal dynamical behaviors of the CSTR.