Open AccessFixed point iteration‐based subspace identification of Hammerstein state‐space models
Author(s) -
Hou Jie,
Chen Fengwei,
Li Penghua,
Zhu Zhiqin
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.6041
Subject(s) - subspace topology , control theory (sociology) , mathematics , singular value decomposition , convergence (economics) , state space , fixed point , linear system , iterative method , identification (biology) , markov chain , mathematical optimization , system identification , computer science , algorithm , measure (data warehouse) , artificial intelligence , mathematical analysis , statistics , botany , control (management) , database , biology , economics , economic growth
In this study, a fixed point iteration‐based subspace identification method is proposed for Hammerstein state‐space systems. The original system is decomposed into two subsystems with fewer parameters based on the hierarchical identification principle. Each subsystem is related directly to either the linear dynamics or the static non‐linearity. A two‐stage least‐squares‐based iterative method is then implemented to separately estimate the coefficients of the non‐linear subsystem and the extended Markov parameters of the linear subsystem. The linear subsystem parameters are extracted from the identified extended Markov parameters using a singular value decomposition based method. Convergence analysis of the proposed method is established using fixed point theory, which shows that the proposed method gives consistent estimates under arbitrary non‐zero initial conditions. Simulation results are included to show the performance of the proposed method.