Identification method for a class of periodic discrete-time dynamic nonlinear systems based on Sinusoidal ESN

In this paper, an improved identification method based on sinusoidal echo state network (SESN) is proposed to identify a class of periodic discrete-time dynamic nonlinear systems with or without noise. For periodic nonlinear systems, the sinusoidal state activation functions can provide more efficient mapping than the sigmoidal state activation functions. A matrix trace based online learning algorithm is constructed to train the output weights of SESN. Based on the Lyapunov stability theory, the asymptotical convergence of the identification error to zero is proved. A nonlinear autoregressive with exogenous (NARX) input model is used to validate the effectiveness of the proposed identification method. (C) 2017 Elsevier B.V. All rights reserved.