Robust Recursive Identification of Hammerstein Models Based on Weiszfald Algorithm

Abstract

The Hammerstein models can accurately describe a wide variety of nonlinear systems (chemical process, power electronics, electrical drives, sticky control valves). Algorithms of identification depend, among other, on the assumption about the nature of stochastic disturbance. Practical research shows that disturbances, owing the presence of outliers, have a non-Gaussian distribution. In such case it is a common practice to use the robust statistics. In the paper, by analysis of the least favourable probability density, it is shown that the robust (Huber`s) estimation criterion can be presented as a sum of non-overlapping - norm and - norm criteria. By using a Weiszfald algorithm - norm criterion is converted to - norm criterion. So, the weighted - norm criterion is obtained for the identification. The main contributions of the paper are: (i) Presentation of the Huber`s criterion as a sum of - norm and - norm criteria; (ii) Using the Weiszfald algorithm – norm criterion is converted to a weighted - norm criterion; (iii) Weighted extended least squares in which robustness is included through weighting coefficients are derived for NARMAX (nonlinear autoregressive moving average with exogenous variable) . The illustration of the behaviour of the proposed algorithm is presented through simulations.