Decoupled Parameter Identification for Network-Based Nonlinear Systems Using Correlation Analysis and Optimal Gradient Theory

For the identification problem of Hammerstein models, this paper proposes a decoupled identification algorithm that combines the correlation analysis with the optimal gradient-based iterative algorithm. The proposed method firstly decouples the linear and the nonlinear subsystems of the Hammerstein model with the help of the correlation analysis. Then, the least squares algorithm is used to estimate the linear parameters. For the nonlinear subsystem, which is represented by a fuzzy neural network, a clustering algorithm is employed to initialize the parameters of the membership functions, so that the fuzzy rules can better reflect the distribution characteristics of the observation data. In the weight identification stage, the optimal gradient theory is introduced into the gradient-based iterative algorithm. Based on the solved optimal step size, the method achieves adaptive parameter updates, which significantly improves convergence speed while maintaining algorithm stability. Finally, the proposed algorithm is applied to two simulations, and the results demonstrate its effectiveness for both linear and nonlinear parameters in Hammerstein models.