Skip to main content
SpringerLink
Log in

Two-stage Gradient-based Recursive Estimation for Nonlinear Models by Using the Data Filtering

International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Cite this article

Abstract

This paper considers the parameter estimation problem of a two-input single-output Hammerstein finite impulse response system with autoregressive moving average noise. Applying the data filtering technique, the input-output data is filtered and the original system with autoregressive moving average noise is changed into the system with moving average noise. Then, based on the key term separation technique, the filtered system is decomposed into two subsystems: one subsystem contains the unknown parameters in the nonlinear block, the other contains the unknown parameters in the linear dynamic block and the noise model. A filtering based multi-innovation stochastic gradient algorithm is presented for Hammerstein finite impulse response systems. The simulation results confirm that the proposed algorithm is effective in estimating the parameters of two-input single-output Hammerstein finite impulse response systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Pan, H. Ma, X. Zhang, Q. Y. Liu, F. Ding, Y. F. Chang, and J. Sheng, “Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises,” IET Signal Processing, vol. 14, no. 7, pp. 455–466, September 2020.

    Article  Google Scholar 

  2. F. Ding, L. Lv, J. Pan, X. K. Wan, and X. B. Jin, “Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data,” International Journal of Control Automation and Systems, vol. 18, no. 4, pp. 886–896, April 2020.

    Article  Google Scholar 

  3. L. J. Wan, “Decomposition- and gradient-based iterative identification algorithms for multivariable systems using the multi-innovation theory,” Circuits Systems and Signal Processing, vol. 38, no. 7, pp. 2971–2991, July 2019.

    Article  Google Scholar 

  4. L. J. Wan, X. M. Liu, F. Ding, and C. P. Chen, “Decomposition least-squares-based iterative identification algorithms for multivariable equation-error autoregressive moving average systems,” Mathematics, vol. 7, no. 7, Article Number: 609, July 2019.

  5. M. H. Li and X. M. Liu, “Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique,” International Journal of Control Automation and Systems, vol. 18, no. 6, pp. 1581–1592, June 2020.

    Article  Google Scholar 

  6. M. H. Li and X. M. Liu, “The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique,” Signal Processing, vo. 147, pp. 23–34, June 2018.

    Article  Google Scholar 

  7. L. J. Wang, Y. Ji, L. J. Wan, and N. Bu, “Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise,” Journal of the Franklin Institute, vol. 356, no. 16, pp. 10102–10122, November 2019.

    Article  MathSciNet  MATH  Google Scholar 

  8. L. J. Wan, F. Ding, X. M. Liu, and C. P. Chen, “A new iterative least squares parameter estimation approach for equation-error autoregressive systems,” International Journal of Control, Automation and Systems, vol. 18, no. 3, pp. 780–790, March 2020.

    Article  Google Scholar 

  9. L. J. Wang, Y. Ji, H. L. Yang, and L. Xu, “Decomposition-based multiinnovation gradient identification algorithms for a special bilinear system based on its input-output representation,” International Journal of Robust and Nonlinear Control, vol. 30, no. 9, pp. 3607–3623, June 2020.

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Ding, L. Xu, D.D. Meng, X. K. Wan, and X. B. Jin, “Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model,” Journal of Computational and Applied Mathematics, vol. 369, p. 112575, May 2020.

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Ji, C. Zhang, Z. Kang, and T. Yu, “Parameter estimation for block-oriented nonlinear systems using the key term separation,” International Journal of Robust and Nonlinear Control, vol. 30, no. 9, pp. 3727–3752, June 2020.

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Ji, X. K. Jiang, and L. J. Wan, “Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems,” Journal of the Franklin Institute, vol. 357, no. 8, pp. 5019–5032, May 2020.

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. M. Fan and X. M. Liu, “Two-stage auxiliary model gradient-based iterative algorithm for the input nonlinear controlled autoregressive system with variable-gain non-linearity,” International Journal of Robust and Nonlinear Control, vol. 30, no. 14, pp. 5492–5509, September 2020.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Cheng, J. H. Park, X. Zhao, H. R. Karimi, and J. Cao, “Quantized nonstationary filtering of network-based Markov switching RSNSs: A multiple hierarchical structure strategy,” IEEE Transactions on Automatic Control, vol. 65, no. 11, pp. 4816–4823, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Chen, Y. Fan, C. X. Zhang, and C. Song, “Sampling-based Event-triggered and Self-triggered Control for Linear Systems,” International Journal of Control Automation and Systems, vol. 18, no. 3, pp. 672–681, March 2020.

    Article  Google Scholar 

  16. A. S. S. Abadi, P. A. Hosseinabadi, and S. Mekhilef, “Fuzzy adaptive fixed-time sliding mode control with state observer for a class of high-order mismatched uncertain systems,” International Journal of Control Automation and Systems, vol. 18, no. 10, pp. 2492–2508, October 2020.

    Article  Google Scholar 

  17. J. Vörös, “Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones,” IEEE Transactions on Automatic Control, vol. 48, no. 12, pp. 2203–2206, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Chen, Y. J. Liu, and L. Xu, “A new filter-based stochastic gradient algorithm for dual-rate ARX models,” International Journal of Adaptive Control and Signal Processing, vol. 32, no. 11, pp. 1557–1568, November 2018.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. F. Zhang, S. P. Zhang, Z. Q. Wang, and B. C. Lu, “Dynamic control allocation algorithm for a class of distributed control systems,” International Journal of Control Automation and Systems, vol. 18, no. 2, pp. 259–270, February 2020.

    Article  Google Scholar 

  20. Y. J. Wang, “Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model,” Automatica, vol. 71, pp. 308–313, September 2016.

    Article  MathSciNet  MATH  Google Scholar 

  21. M. H. Li and X. M. Liu, “The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 7, pp. 1189–1211, July 2019.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Cheng, J. H. Park, J. Cao, and W. Qi, “A hidden mode observation approach to finite-time SOFC of Markovian switching systems with quantization,” Nonlinear Dynamics, vol. 100, no. 1, pp. 509–521, February 2020.

    Article  MATH  Google Scholar 

  23. J. Cheng, D. Zhang, W. Qi, J. Cao, and K. Shi, “Finite-time stabilization of T-S fuzzy semi-Markov switching systems: A coupling memory sampled-data control approach,” Journal of The Franklin Institute, vol. 357, no. 16, pp. 11265–11280, November 2020.

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Xu, L. Chen, and W. L. Xiong, “Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration,” Nonlinear Dynamics, vol. 79, no. 3, pp. 2155–2163, February 2015.

    Article  MathSciNet  Google Scholar 

  25. L. Xu, “The damping iterative parameter identification method for dynamical systems based on the sine signal measurement,” Signal Processing, vol. 120, pp. 660–667, March 2016.

    Article  Google Scholar 

  26. E. W. Bai and K. Li, “Convergence of the iterative algorithm for a general Hammerstein system identification,” Automatica, vol. 46, no. 11, pp. 1891–1896, November 2010.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Chen, Y. J. Liu, and X. H. Wang, “Recursive least squares algorithm for nonlinear dual-rate systems using missing-output estimation model,” Circuits Systems Signal Process, vol. 36, no. 4, pp. 1406–1425, April 2017.

    Article  MathSciNet  MATH  Google Scholar 

  28. L. Xu and G. L. Song, “A recursive parameter estimation algorithm for modeling signals with multi-frequencies,” Circuits Systems and Signal Processing, vol. 39, no. 8, pp. 4198–4224, August 2020.

    Article  MATH  Google Scholar 

  29. L. Xu, W. L. Xiong, A. Alsaedi, and T. Hayat, “Hierarchical parameter estimation for the frequency response based on the dynamical window data,” International Journal of Control Automation and Systems, vol. 16, no. 4, pp. 1756–1764, August 2018.

    Article  Google Scholar 

  30. F. Ding, X. Zhang, and L. Xu, “The innovation algorithms for multivariable state-space models,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 11, pp. 1601–1608, November 2019.

    Article  MathSciNet  MATH  Google Scholar 

  31. L. Xu, “Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling,” Circuits Systems Signal Process, vol. 36, no. 4, pp. 1735–1753, April 2017.

    Article  MATH  Google Scholar 

  32. L. Xu, “Parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle,” IET Signal Processing, vol. 11, no. 2, pp. 228–237, April 2017.

    Article  Google Scholar 

  33. Y. Ji and Z. Kang, “Three-stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 31, no. 3, pp. 971–987, 2021.

    Article  MathSciNet  Google Scholar 

  34. C. M. Jiang, A. Zada, M. T. Senel, and T. X. Li, “Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure,” Advances in Difference Equations, vol. 2019, no. 1, Article Number: 456, October 2019.

  35. X. Zhang, “Adaptive parameter estimation for a general dynamical system with unknown states,” International Journal of Robust and Nonlinear Control, vol. 30, no. 4, pp. 1351–1372, March 2020.

    Article  MathSciNet  MATH  Google Scholar 

  36. X. Zhang, F. Ding, and L. Xu, “Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 30, no. 4, pp. 1373–1393, March 2020.

    Article  MathSciNet  MATH  Google Scholar 

  37. X. Zhang, F. Ding, L. Xu, and E. F. Yang, “Highly computationally efficient state filter based on the delta operator,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 6, pp. 875–889, June 2019.

    Article  MathSciNet  MATH  Google Scholar 

  38. X. Zhang, F. Ding, and E. F. Yang, “State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 7, pp. 1157–1173, July 2019.

    Article  MathSciNet  MATH  Google Scholar 

  39. Y. Gu, Q. Zhu, and H. Nouri, “Bias compensation-based parameter and state estimation for a class of time-delay nonlinear state-space models,” IET Control Theory and Applications, vol. 14, no. 15, pp. 2176–2185, October 2020.

    Article  Google Scholar 

  40. N. Bu, J. X. Pang, and M. Deng, “Robust fault tolerant tracking control for the multi-joint manipulator based on operator theory,” Journal of the Franklin Institute, vol. 357, no. 5, pp. 2696–2714, March 2020.

    Article  MathSciNet  MATH  Google Scholar 

  41. Y. M. Zhou and S. J. Mei, “Effects of PEDOT:PSS:GO composite hole transport layer on the luminescence of perovskite light-emitting diodes,” RSC Advances, vol. 10, no. 44, pp. 26381–26387, 2020.

    Article  Google Scholar 

  42. L. J. Wang, “Hybrid model predictive control strategy of supercapacitor energy storage system based on double active bridge,” Energies, vol. 12, no. 11, 2134, June 2019.

    Article  Google Scholar 

  43. Y. Zhang, “Capacity allocation of HESS in micro-grid based on ABC algorithm,” International Journal of Low-Carbon Technologies, vol. 15, no. 4, pp. 496–505, November 2020.

    Article  Google Scholar 

  44. X. Zhang, “Hierarchical parameter and state estimation for bilinear systems,” International Journal of Systems Science, vol. 51, no. 2, 275–290, 2020.

    Article  MathSciNet  Google Scholar 

  45. X. Zhang, F. Ding, L. Xu, and E. F. Yang, “State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle,” IET Control Theory and Applications, vol. 12, no. 12, pp. 1704–1713, August 2018.

    Article  MathSciNet  Google Scholar 

  46. X. Zhang, “Recursive parameter estimation and its convergence for bilinear systems,” IET Control Theory and Applications, vol. 14, no. 5, pp. 677–688, March 2020.

    Article  Google Scholar 

  47. X. Zhang, Q. Y. Liu, F. Ding, A. Alsaedi, and T. Hayat, “Recursive identification of bilinear time-delay systems through the redundant rule,” Journal of the Franklin Institute, vol. 357, no. 1, pp. 726–747, January 2020.

    Article  MathSciNet  MATH  Google Scholar 

  48. F. Ji, L. Liao, T. Z. Wu, C. Chang, and M. N. Wang, “Self-reconfiguration batteries with stable voltage during the full cycle without the DC-DC converter,” Journal of Energy Storage, vol. 28, Article Number: 101213, April 2020.

  49. X. K. Wan, Z. Y. Jin, H. B. Wu, J. J. Liu, B. R. Zhu, and H. G. Xie, “Heartbeat classification algorithm based on one-dimensional convolution neural network,” Journal of Mechanics in Medicine and Biology, vol. 20, no. 7, Article Number: 2050046, September 2020.

  50. N. Zhao, Y. Liang, D. Niyato, Y. Pei, M. Wu, and Y. Jiang, “Deep reinforcement learning for user association and resource allocation in heterogeneous cellular networks,” IEEE Transactions on Wireless Communications, vol. 18, no. 11, pp. 5141–5152, November 2019.

    Article  Google Scholar 

  51. Y. Zhang, Z. Yan, C. C. Zhou, T. Z. Wu, and Y. Y. Wang, “Capacity allocation of HESS in micro-grid based on ABC algorithm,” International Journal of Low-Carbon Technologies, vol. 15, no. 4, pp. 495–505, 2020.

    Google Scholar 

  52. Z. Y. Zhao, X. Y. Wang, P. Yao, and Y. T. Bai, “A health performance evaluation method of multirotors under wind turbulence,” Nonlinear Dynamics, vol. 102, pp. 1701–1715, 2020.

    Article  Google Scholar 

  53. G. C. Yang, Z. J. Chen, Y. Li, and Z. D. Su, “Rapid relocation method for mobile robot based on improved ORB-SLAM2 algorithm,” Remote Sensing, vol. 11, no. 2, Article Number: 149, January 2019.

  54. S. Su, X. K. Wang, Y. Cao, and J. T. Yin, “An energy-efficient train operation approach by integrating the metro timetabling and eco-driving,” IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 10, pp. 4252–4268, October 2020.

    Article  Google Scholar 

  55. S. Su, T. Tang, J. Xun, F. Cao, and Y. H. Wang, “Design of running grades for energy-efficient train regulation: A case study for beijing yizhuang line,” IEEE Intelligent Transportation Systems Magazine, vol. 13, no. 2, 189–200, February 2021.

    Article  Google Scholar 

  56. Y. Cao, Z. Wang, F. Liu, P. Li, and G. Xie, “Bio-inspired speed curve optimization and sliding mode tracking control for subway trains,” IEEE Transactions on Vehicular Technology, vol. 68, no. 7, pp. 6331–6342, July 2019.

    Article  Google Scholar 

  57. Y. Cao, Y. K. Sun, G. Xie, and T. Wen, “Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy,” IEEE Transactions on Vehicular Technology, vol. 68, no. 8, pp. 7544–7551, August 2019.

    Article  Google Scholar 

  58. H. Ma, X. Zhang, and Q.Y. Liu, “Partiallly-coupled gradient-based iterative algorithms for multivariable output-error-like systems with autoregressive moving average noises,” IET Control Theory and Applications, vol. 14, no. 17, pp. 2613–2627, November 2020.

    Article  Google Scholar 

  59. M.H. Wu, “Object detection based on RGC mask R-CNN,” IET Image Processing, vol. 14, no. 8, pp. 1502–1508, June 2020.

    Article  Google Scholar 

  60. Y. Cao, P. Li, and Y. Zhang, “Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing,” Future Generation Computer Systems, vol. 88, pp. 279–283, November 2018.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P. R. China

    Yan Ji, Zhen Kang & Chen Zhang

Authors
  1. Yan Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Ji.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This paper was supported by the National Natural Science Foundation of China (No. 61472195 and 61773356), and the Natural Science Foundation of Shandong Province (No. ZR2020MF160).

Yan Ji received her Ph.D. degree from the School of Communication and Control Engineering, Jiangnan University (Wuxi, China) in 2010. She has been an Associate Professor in the College of Automation and Electronic Engineering, Qingdao University of Science and Technology. Her research interests include control of complex networks, system identification and process control.

Zhen Kang was born in Jinan, Shandong Province in November 1993. He is currently a master student in the College of Automation and Electronic Engineering at the Qingdao University of Science and Technology (Qingdao, China). His research interests include system identification and parameter estimation.

Chen Zhang was born in Dezhou, Shandong Province in April 1994. He received his B.Sc. degree from the School of School of Mechanical and Control Engineering at the Shengli College at the China University Of Petroleum (Dongying, China) in 2017. He is currently a master student in the College of Automation and Electronic Engineering at the Qingdao University of Science and Technology (Qingdao, China). His research interests include system identification and parameter estimation.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ji, Y., Kang, Z. & Zhang, C. Two-stage Gradient-based Recursive Estimation for Nonlinear Models by Using the Data Filtering. Int. J. Control Autom. Syst. 19, 2706–2715 (2021). https://doi.org/10.1007/s12555-019-1060-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-1060-y

Keywords

search

Navigation