Parameter Learning for the Hammerstein Output Error System with Time-delay State-space Model

This paper discusses a scheme for identifying the Hammerstein output error system with time-delay state-space model. The Hammerstein system is composed of a static nonlinear block approximated by neural fuzzy model and a dynamical linear block modeled by time-delay state-space model, and the parameters learning separation of the Hammerstein system is realized by using special test signal composed of Gaussian signal and random signal. Firstly, according to the properties of unit backward operator, the state space system can be transformed into a transfer function, and the parameters of the linear block can be estimated by the virtue of correlation analysis method based on measurement input-output data of Gaussian signals. In addition, based on random signals, the parameters of static nonlinear block and noise model are learned by using the recursive extended least square algorithm. Simulation results show that the scheme proposed can effectively learn the time-delay-based Hammerstein state-space system and get high learning accuracy.