Recursive Least Squares Algorithm with Variable Forgetting Factor for Identification in Hammerstein System

The paper studies the identification of single-input single-output nonlinear Hammerstein systems， and proposes a variable forgetting factor recursive least squares algorithm. Due to the nonlinear characteristics of the Hammerstein system model， the traditional recursive least squares algorithm cannot be directly used to solve the identification problem of the system. In order to solve this problem， the Hammerstein system parameters are mapped and transformed so that the transformed system parameters and the input and output of the Hammerstein system form a linear relationship. In this way， the system can be applied to the recursive least squares algorithm； Moreover， in order to solve the problem of the decrease in convergence speed caused by parameter mapping， the paper further proposes a recursive least squares algorithm with variable forgetting factor. The simulation results show that the proposed algorithm can obtain better convergence and stability， and improve the system identification accuracy.