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A global convergent outlier robust adaptive predictor for MIMO Hammerstein models
Author(s) -
Filipovic Vojislav Z.
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3705
Subject(s) - outlier , mimo , mathematics , nonlinear system , convergence (economics) , scalar (mathematics) , martingale (probability theory) , polynomial , a priori and a posteriori , mathematical optimization , control theory (sociology) , algorithm , computer science , statistics , artificial intelligence , beamforming , mathematical analysis , philosophy , physics , geometry , control (management) , epistemology , quantum mechanics , economics , economic growth
Summary The 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.