Weighted Learning Identification Method for Hammerstein Nonlinear Time-varying Systems

For Hammerstein nonlinear time-varying systems running repeatedly on finite intervals, a weighted iterative learning algorithm is proposed to estimate the time-varying parameters involved in the system dynamics. The nonlinear input part of the Hammerstein system is tackled based on polynomial expansion, and the iterative learning least square algorithm is given for the time-varying parameter identification. In order to prevent data saturation, an iterative learning least squares algorithm with forgetting factor is proposed for reducing the system tracking error and improving the identification accuracy; A weighted iterative learning least squares algorithm is further presented by introducing the weight matrix. The derivations of the three algorithms are given in detail. The simulation results demonstrate the effectiveness of the proposed learning algorithms, and in comparison with iterative learning least squares algorithm, the modified one sreach high identification accuracy and need fewer iterations.