Fixed point iteration‐based subspace identification of Hammerstein state‐space models

Abstract

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.