An adaptive second order fuzzy neural network for nonlinear system modeling

In this paper, an adaptive second order algorithm (ASOA) has been developed to train the fuzzy neural network (FNN) to achieve fast and robust convergence for nonlinear system modeling. Different from recent studies, this ASOA-based FNN (ASOA-FNN) has the quasi Hessian matrix and gradient vector which are accumulated as the sum of related sub matrices and vectors, respectively. Meanwhile, the learning rate of ASOA-FNN is designed to accelerate the learning speed. In addition, the convergence of the proposed ASOA-FNN has been proved both in the fixed learning rate phase and the adaptive learning rate phase. Finally, several comparisons have been realized and they have shown that the proposed ASOA-FNN has faster convergence speed and more accurate results than that of some existing methods.