A new convergence condition for discrete-time nonlinear system identification using a Hopfield neural network

This paper presents a method of discrete time nonlinear system identification using a HopfieId neural network (HNN) as a coefficient learning mechanism to obtain optimized coefficients over a set of Gaussian basis functions. A linear combination of Gaussian basis functions is used to replace the nonlinear function of the equivalent discrete time nonlinear system. The outputs of the HNN, which are coefficients over a set of Gaussian basis functions, are discretized to be a discrete Hopfield learning model. Using the outputs of the HNN, one can obtain the optimized coefficients of the linear combination of Gaussian basis functions conditional on properly choosing an activation function scaling factor of the HNN. The main contributions of this paper is that the convergence of learning of the HNN can be guaranteed if the activation function scaling factor is properly chosen. Finally, to demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.