Hierarchical Newton iterative identification methods for a class of input multi-piecewise Hammerstein models with autoregressive noise

Advancements in mathematical theories and applied technologies have driven research on modeling and identification of complex nonlinear systems, yet existing models still face challenges in terms of model structures, accuracy of parameter estimation, and efficiency. In this study, we present a class of input multi-piecewise Hammerstein models that utilize piecewise-linear function to capture arbitrary nonlinear characteristics. By employing the key term separation technique and the Newton iterative algorithm for parameter estimation, a generalized Newton iterative algorithm is proposed, which overcomes the limitations of conventional identification methods in handling complex nonlinearities. Additionally, considering the computational load caused by the numerous parameters in multi-piecewise linear function and the inversion of the Hessian matrix in the Newton iterative algorithm, the hierarchical identification principle is introduced and a three-stage generalized Newton iterative algorithm is derived for enhancing the computational efficiency. The feasibility of the presented methods are demonstrated through a simulation example.