Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

2.10

CiteScore

Fang QiuThis email address is being protected from spambots. You need JavaScript enabled to view it., Haixu Zhang, and Yan Ji

College of Science, Shandong University of Aeronautics, Binzhou 256600, China


 

 

Received: September 9, 2023
Accepted: January 14, 2024
Publication Date: March 2, 2024

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.


Download Citation: ||https://doi.org/10.6180/jase.202412_27(12).0014  


This paper mainly studies the identification problem of the single-output two-input error system. A hierarchical least squares algorithm is derived by combining the model decomposition skill and the principle of hierarchical identification. The basic idea of the derived identification method is to decompose the system into two subsystems and identify the parameter vector of each subsystem separately. Compared with the auxiliary model least squares (AM-RLS) algorithm, the proposed two-stage recursive least squares (TS-RLS) algorithm has lower computational cost and higher estimation accuracy. Furthermore, the convergence of the TS-RLS algorithm is analyzed, which can guarantee the stability of the algorithm and make it more suitable for various practical application scenarios. Finally, a numerical example is presented to illustrate the validity of the derived approach.


Keywords: Error class system; Ancillary model; Least squares method; Hierarchical least squares algorithm


  1. [1] N. Li, S. Guo, and Y. Wang, (2019) “Weighted preliminary-summation-based principal component analysis for non-Gaussian processes" Control engineering practice 87: 122–132. DOI: 10.1016/j.conengprac.2019.03.015.
  2. [2] X. Zhang, F. Ding, and E. Yang, (2019) “State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors" International journal of adaptive control and signal processing 33: 1157–1173. DOI: 10.1002/acs.3027.
  3. [3] J. Ding, J. Chen, J. Lin, and G. Jiang, (2019) “Particle filtering-based recursive identification for controlled autoregressive systems with quantized output" IET control theory applications 13: 2181–2187. DOI: 10.1049/ietcta.2019.0028.
  4. [4] E. Pieter, (1974) “System identification : parameter and state estimation":
  5. [5] F. Ding and T. Chen, (2005) “Hierarchical gradientbased identification of multivariable discrete-time systems" Automatica 41: 315–325. DOI: 10.1016/j.automatica.2004.10.010.
  6. [6] F. Ding and T. Chen, (2005) “Hierarchical identification of lifted state-space models for general dual-rate systems" IEEE transactions on circuits and systems, I 52: 1179–1187. DOI: 10.1109/TCSI.2005.849144.
  7. [7] Y. Liu, F. Ding, and Y. Shi, (2014) “An efficient hierarchical identification method for general dual-rate sampleddata systems" Automatica 50: 962–970. DOI: 10.1016/j.automatica.2013.12.025.
  8. [8] M. Li and X. Liu, (2018) “The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique" Signal Processing 147: 23–34. DOI: 10.1016/j.sigpro.2018.01.012.
  9. [9] F. Ding, F. Wang, L. Xu, T. Hayat, and A. Alsaedi, (2018) “Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique" IET control theory applications 11: 390–400. DOI: 10.1049/iet-cta.2016.0491.
  10. [10] D. Yang and F. Ding, (2023) “Multi-innovation gradientbased iterative identification Methods for feedback nonlinear systems by using the decomposition technique" International Journal Of Robust And Nonlinear Control 33: 7755–7773. DOI: 10.1002/rnc.6796.
  11. [11] F. Ding and T. Chen, (2004) “Combined parameter and output estimating of dual-rate systems using an auxiliary model" Automatica 40: 1739–1748. DOI: 10.1016/j.automatica.2004.05.001.
  12. [12] Y. Wang and F. Ding, (2016) “Novel data filtering based parameter identification for multiple-input multipleoutput systems using the auxiliary model" Automatica 71: 308–313. DOI: 10.1016/j.automatica.2016.05.024.
  13. [13] X. Wang, F. Ding, A. Alsaedi, and T. Hayat, (2021) “Auxiliary model-based iterative parameter estimation for a nonlinear output-error system with saturation and deadzone nonlinearity" International Journal of Robust and Nonlinear Control 31: 4262–4286. DOI: 10.1002/rnc.5468.
  14. [14] J. Ma, W. Xiong, J. Chen, and F. Ding, (2017) “Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter" IET control theory applications 11: 857–869. DOI: 10.1049/ietcta.2016.1033.
  15. [15] L. Xu, F. Ding, X. Lu, L. Wan, and J. Sheng, (2020) “Hierarchical multi-innovation generalized extended stochastic gradient methods for multivariable equation-error autoregressive moving average systems" IET control theory applications 14: 1276–1286. DOI: 10.1049/ietcta.2019.0731.
  16. [16] Y. Ji, X. Jiang, and L. Wan, (2020) “Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems" Journal of the Franklin Institute 357: 5019–5032. DOI: 10.1016/j.jfranklin.2020.03.027.
  17. [17] Y. Ji, Z. Kang, and C. Zhang, (2021) “Two-stage Gradient-based Recursive Estimation for Nonlinear Models by Using the Data Filtering" International Journal of Control, Automation and Systems 19: 2706–2715. DOI: 10.1007/s12555-019-1060-y.
  18. [18] Y. Zhou, F. Ding, and E. Yang, (2021) “Two-stage extended recursive gradient algorithm for locally linear RBFbased autoregressive models with colored noises" ISA transactions 129: 284–294. DOI: 10.1016/j.isatra.2022.02.011.
  19. [19] Y. Ji and Z. Kang, (2021) “Three-stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems" International Journal of Robust and Nonlinear Control 31: 971–987. DOI: 10.1002/rnc.5323.
  20. [20] F. Ding, H. Ma, J. Pan, and E. Yang, (2021) “Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation" Journal of the Franklin Institute 358: 5113–5135. DOI: 10.1016/j.jfranklin.2021.04.006.
  21. [21] Y. Fan and X. Liu, (2022) “Auxiliary model-based multiinnovation recursive identification algorithms for an input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity" International Journal of Adaptive Control and Signal 36: 521–540. DOI: 10.1002/acs.3354.
  22. [22] L. Xu, F. Ding, and E. Yang, (2021) “Auxiliary model multi-innovation stochastic gradient parameter estimation methods for nonlinear sandwich systems" International Journal of Robust and Nonlinear Control 31: 1–18. DOI: 10.1002/rnc.5266.
  23. [23] L. Wang, F. Ding, and P. X. Liu, (2007) “Convergence of HLS estimation algorithms for multivariable ARX-like systems" Applied mathematics and computation 190: 1081–1093. DOI: 10.1016/j.amc.2007.01.089.


    



 

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