This paper proposes a uniform method for identifying four model types of high-order discrete-time nonlinear systems using a Hopfield neural network (HNN) as a coefficient learning mechanism to obtain optimized coefficients over a set of Gaussian basis functions. Four model types of discrete-time plants chosen for their generality as well as for their analytical tractability are suggested in this paper. The outputs of the HNN, which are coefficients over a set of Gaussian basis functions, are discretized to be a discrete Hopfield learning model and completely approximated by the learning model if the sampled step size approaches zero. Through the HNN, obtaining the optimized coefficients of the linear combination of Gaussian basis functions depends on properly choosing an activation function scaling factor. The main result of this paper is that the configurations of the HNN learning mechanism and the convergence conditions for the four model types of nonlinear systems are derived and found to be analogous. The convergence condition provides a lower-bound which guarantees that the discrete Hopfield learning model behaves similarly to the gradient descent learning algorithm, and an upper-bound which guarantees the convergence of the learning methods. Finally, to demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.
Relation:
Dynamics of Continuous, Discrete and Impulsive Systems, Series B 14, p.57-66
