Hierarchical estimation method for fractional-order systems based on the auxiliary model - Zhang, Yufan; Zhang, Xiao; Ding, Feng (Applied mathematics and computation, 2026)
•A hierarchical least squares algorithm is proposed to study the identification of the fractional Hammerstein-Wiener system.•Using the hierarchical identification principle, the whole identification process is decomposed into several stages to estimate the parameters of the system.•To handle immeasurable variables, we design an auxiliary model, allowing these variables to be replaced by measurable-based approximations.•We propose a novel auxiliary model-based hierarchical recursive least squares identification algorithm, which updates parameters online as new samples arrive. This ensures improved computational efficiency, reduced computational burden, and enhanced estimation accuracy. This paper investigates the identification of nonlinear fractional Hammerstein-Wiener systems. Considering the coupled terms of the system, the over-parametrization method is used for obtaining a linearly parameterized form with the cross-products between the parameters. To enhance the computational efficiency, a novel least squares algorithm is presented by applying the hierarchical identification principle. The main idea is to decompose the original system into several subsystems to simultaneously estimate the coupled parameters. For the unknown variables, the auxiliary model is constructed and the immeasurable variables are replaced with the outputs of the auxiliary model. Then an auxiliary model based hierarchical least squares algorithm is proposed to identify the parameters of the fractional-order systems. The computational analysis and simulation results validate the performance of the proposed algorithms.