Modelling of nonlinear stochastic dynamical systems using neurofuzzy networks

Abstract

Though a nonlinear stochastic dynamical system can be approximated by feedforward neural networks, the dimension of the input space of the network may be too large, making it to be of little practical importance. The Nonlinear Autoregressive Moving Average model with eXogenous input (NARMAX) is shown to be able to represent a nonlinear stochastic dynamical system under certain conditions. As the dimension of the input space is finite, it can be readily applied in a practical application. It is well known that the training of recurrent networks using the gradient method has a slow convergence rate. In this paper, a fast training algorithm based on the Newton-Raphson method for a recurrent neurofuzzy network with NARMAX structure is presented. The convergence and the uniqueness of the proposed training algorithm are established. A simulation example involving a nonlinear dynamical system corrupted with the correlated noise and a sinusoidal disturbance is used to illustrate the performance of the proposed training algorithm.