A global convergent outlier robust adaptive predictor for MIMO Hammerstein models

Abstract

SummaryThe paper considers the outlier‐robust recursive stochastic approximation algorithm for adaptive prediction of multiple‐input multiple‐output (MIMO) Hammerstein model with a static nonlinear block in polynomial form and a linear block is output error (OE) model. It is assumed that there is a priori information about a distribution class to which a real disturbance belongs. Within the framework of these assumptions, the main contributions of this paper are: (i) for MIMO Hammerstein OE model, the stochastic approximation algorithm, based on robust statistics (in the sense of Huber), is derived; (ii) scalar gain of algorithm is exactly determined using the Laplace function; and (iii) a global convergence of robust adaptive predictor is proved. The proof is based on martingale theory and generalized strictly positive real conditions. Practical behavior of algorithm was illustrated by simulations. Copyright © 2016 John Wiley & Sons, Ltd.