Iterative parameter estimation for a class of fractional-order Hammerstein nonlinear systems disturbed by colored noise

Considering the existence of nonlinearity and fractional-order phenomena in practical environments, this paper investigates the parameter estimation methods for a class of fractional-order Hammerstein nonlinear systems disturbed by colored noise. The methods are based on the decomposition strategy, separating the identification of fractional-order from the identification of system parameters. Meanwhile, the system is divided into two subsystems, which are a linear block system and a nonlinear block system by using the hierarchical identification principle. To overcome the problem of redundant parameter estimation, the over-parameterization method and the key item separation method are used, respectively. Then, a two-stage over-parameterization gradient-based iterative algorithm and a key term separation two-stage gradient-based iterative algorithm are derived, which the auxiliary model is used to compute the unmeasurable variables. In addition, we analyze the computational efficiencies of the proposed algorithms. The simulation results indicate that the proposed algorithms are effective. Finally, the proposed method is evaluated through a battery model. The results show well agreement with the real system outputs.