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Hierarchical estimation method for fractional-order systems based on the auxiliary model

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  • Zhang, Yufan
  • Zhang, Xiao
  • Ding, Feng

Abstract

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.

Suggested Citation

  • Zhang, Yufan & Zhang, Xiao & Ding, Feng, 2026. "Hierarchical estimation method for fractional-order systems based on the auxiliary model," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    • Handle: RePEc:eee:apmaco:v:512:y:2026:i:c:s0096300325004746
    DOI: 10.1016/j.amc.2025.129749
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    References listed on IDEAS

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    1. Ling Xu & Huan Xu & Chun Wei & Feng Ding & Quanmin Zhu, 2024. "The filtering-based recursive least squares identification and convergence analysis for nonlinear feedback control systems with coloured noises," International Journal of Systems Science, Taylor & Francis Journals, vol. 55(16), pages 3461-3484, December.
    2. Qibing Jin & Bin Wang & Zeyu Wang, 2022. "Recursive Identification for MIMO Fractional-Order Hammerstein Model Based on AIAGS," Mathematics, MDPI, vol. 10(2), pages 1-21, January.
    3. Fan, Yamin & Liu, Ximei & Li, Meihang, 2025. "Hierarchical Newton iterative identification methods for a class of input multi-piecewise Hammerstein models with autoregressive noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 237(C), pages 247-262.
    4. Wang, Junwei & Xiong, Weili & Ding, Feng & Zhou, Yihong & Yang, Erfu, 2025. "Parameter estimation method for separable fractional-order Hammerstein nonlinear systems based on the on-line measurements," Applied Mathematics and Computation, Elsevier, vol. 488(C).
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    1. Fan, Yamin & Liu, Ximei & Li, Meihang, 2025. "Hierarchical Newton iterative identification methods for a class of input multi-piecewise Hammerstein models with autoregressive noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 237(C), pages 247-262.

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