Skip to main content
SpringerLink
Log in

Separable Recursive Gradient Algorithm for Dynamical Systems Based on the Impulse Response Signals

  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

The identification for process control systems is considered in this paper based on the impulse response signals from the discrete measurements. By taking advantage of impulse signals and through the model parameter decomposition, two dependent identification models are constructed and two identification sub-algorithms are presented based on the nonlinear gradient optimization. In terms of the associated items of the parameters to be estimated between two derived sub-algorithms, a separable recursive gradient parameter estimation method is proposed by designing an interactive and recursive estimation. The performance tests and the comparison experiments are carried out by the simulation examples.

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. M. Gan, C. L. P. Chen, G. Y. Chen, and L. Chen, “On some separated algorithms for separable nonlinear squares problems,” IEEE Transactions on Cybernetics, vol. 48, no. 10, pp. 2866–2874, October 2018.

    Google Scholar 

  2. L. Xu and F. Ding, “Parameter estimation for control systems based on impulse responses,” International Journal of Control, Automation, and Systems, vol. 15, no. 6, pp. 2471–2479, 2017.

    Google Scholar 

  3. G. Y. Chen, M. Gan, C. L. P. Chen, and H. X. Li, “A regularized variable projection algorithm for separable nonlinear least-squares problems,” IEEE Transactions on Automatic Control, vol. 64, no. 2, pp. 526–537, February 2019.

    MathSciNet  MATH  Google Scholar 

  4. H. Ma, J. Pan, F. Ding, L. Xu, and W. Ding, “Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems,” IET Control Theory and Applications, vol. 13, no. 18, pp. 3040–3051, December 2019.

    Google Scholar 

  5. J. Ding, J. Z. Chen, J. X. Lin, and L. J. Wan, “Particle filtering based parameter estimation for systems with output-error type model structures,” Journal of the Franklin Institute, vol. 356, no. 10, pp. 5521–5540, July 2019.

    MathSciNet  MATH  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, vol. 147, pp. 23–34, June 2018.

    Google Scholar 

  7. J. X. Ma, W. L. Xiong, and J. Chen, “Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter,” IET Control Theory and Applications, vol. 11, no. 6, pp. 857–869, April 2017.

    MathSciNet  Google Scholar 

  8. Y. Gu, Y. Chou, J. Liu, and Y. Ji, “Moving horizon estimation for multirate systems with time-varying time-delays,” Journal of the Franklin Institute, vol. 356, no. 4, pp. 2325–2345, March 2019.

    MathSciNet  MATH  Google Scholar 

  9. M. Gan, H. X. Li, and H. Peng, “A variable projection approach for efficient estimation of RBF-ARX model,” IEEE Transactions on Cybernetics, vol. 45, no. 3, pp. 476–485, March 2015.

    Google Scholar 

  10. 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.

    MathSciNet  MATH  Google Scholar 

  11. J. X. Ma and F. Ding, “Filtering-based multistage recursive identification algorithm for an input nonlinear output-error autoregressive system by using key the term separation technique,” Circuits Systems and Signal Processing, vol. 36, no. 2, pp. 577–599, February 2017.

    MATH  Google Scholar 

  12. F. Ding, F. F. Wang, L. Xu, and M. H. Wu, “Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1321–1339, February 2017.

    MathSciNet  MATH  Google Scholar 

  13. C. Q. Guo, L. J. Wang, and F. Deng, “The auxiliary model based hierarchical estimation algorithms for bilinear stochastic systems with colored noises,” International Journal of Control Automation and Systems, vol. 18, no. 3, pp. 650–660, March 2020.

    Google Scholar 

  14. M. H. Li, X. M. Liu, and F. Ding, “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.

    MathSciNet  MATH  Google Scholar 

  15. X. K. Wan, Y. Li, C. Xia, M. H. Wu, J. Liang, and N. Wang, “A T-wave alternans assessment method based on least squares curve fitting technique,” Measurement, vol. 86, pp. 93–100, May 2016.

    Google Scholar 

  16. J. Pan, W. Li, and H. P. Zhang, “Control algorithms of mag-netic suspension systems based on the improved double exponential reaching law of sliding mode control,” International Journal of Control Automation and Systems, vol. 16, No. 6, pp. 2878–2887, December 2018.

    Google Scholar 

  17. L. Geng and R. B. Xiao, “Control and backbone identification for the resilient recovery of a supply network utilizing outer synchronization,” Applied Sciences, vol. 10, no. 1, p. 313, January 2020.

    Google Scholar 

  18. L. Tang, G. J. Liu, M. Yang, F. Y. Li, F. P. Ye, and C. Y. Li, “Joint design and torque feedback experiment of rehabilitation robot,” Advances in Mechanical Engineering, vol. 12, no. 5, pp. 1–11, May 2020.

    Google Scholar 

  19. M. Gan, C. L. P. Chen, G. Y. Chen, and L. Chen, “On some separated algorithm for separable nonlinear least squares problems,” IEEE Transaction on Cybernetics, vol. 48, no. 10, pp. 2866–2874, 2018.

    Google Scholar 

  20. Y. J. Wang, F. Ding, and M. H. Wu, “Recursive parameter estimation algorithm for multivariate output-error systems,” Journal of the Franklin Institute, vol. 355, no. 12, pp. 5163–5181, August 2018.

    MathSciNet  MATH  Google Scholar 

  21. P. Ma and F. Ding, “New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1568–1583, February 2017.

    MathSciNet  MATH  Google Scholar 

  22. C. P. Yu, L. Ljung, A. Wills, and M. Verhaegen, “Constrained subspace method for the identification of structured state-space models,” IEEE Transactions on Automatic Control, 2020. DOI: https://doi.org/10.1109/TAC.2019.2957703

  23. J. Pan, X. Jiang, X. K. Wan, and W. Ding, “A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems,” International Journal of Control Automation and Systems, vol. 15, no. 3, pp. 1189–1197, 2017.

    Google Scholar 

  24. J. Ding, J. Z. Chen, J. X. Lin, and G. P. Jiang, “Particle filtering-based recursive identification for controlled auto-regressive systems with quantised output,” IET Control Theory and Applications, vol. 13, no. 14, pp. 2181–2187, September 2019.

    Google Scholar 

  25. L. J. Wan and F. Ding, “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.

    Google Scholar 

  26. 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.

    Google Scholar 

  27. 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.

    Google Scholar 

  28. S. Y. Liu, F. Ding, L. Xu, and T. Hayat, “Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals,” Circuits Systems and Signal Processing, vol. 38, no. 7, pp. 3251–3268, July 2019.

    Google Scholar 

  29. Y. Cao, H. Lu, and T. Wen, “A safety computer system based on multi-sensor data processing,” Sensors, vol. 19, no. 4, 818, February 2019.

    Google Scholar 

  30. Y. Cao, Y. Zhang, T. Wen, and P. Li, “Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high-speed train control system,” Chaos, vol. 29, no. 1, p. 013130, January 2019.

    Google Scholar 

  31. L. J. Liu, F. Ding, L. Xu, J. Pan, A. Alsaedi, and T. Hayat, “Maximum likelihood recursive identification for the multivariate equation-error autoregressive moving average systems using the data filtering,” IEEE Access, vol. 7, pp. 41154–41163, 2019.

    Google Scholar 

  32. C. C. Yin and C. W. Wang, “The perturbed compound Poisson risk process with investment and debit interest,” Methodology and Computing in Applied Probability, vol. 12, no. 3, pp. 391–413, September 2010.

    MathSciNet  MATH  Google Scholar 

  33. C. C. Yin and K. C. Yuen, “Optimality of the threshold dividend strategy for the compound Poisson model,” Statistics & Probability Letters, vol. 81, no. 12, pp. 1841–1846, December 2011.

    MathSciNet  MATH  Google Scholar 

  34. C. C. Yin and Y. Z. Wen, “Optimal dividend problem with a terminal value for spectrally positive Levy processes,” Insurance Mathematics & Economics, vol. 53, no. 3, pp. 769–773, November 2013.

    MathSciNet  MATH  Google Scholar 

  35. C. C. Yin and Y. Z. Wen, “Exit problems for jump processes with applications to dividend problems,” Journal of Computational and Applied Mathematics, vol. 245, pp. 30–52, June 2013.

    MathSciNet  MATH  Google Scholar 

  36. F. Yang, J. L. Fu, and X. X. Li, “A potential-free field inverse Schroinger problem: optimal error bound analysis and regularization method,” Inverse Problems in Science and Engineering, 2019. DOI: https://doi.org/10.1080/17415977.2019.1700243

  37. F. Yang, N. Wang, and X. X. Li, “Landweber iterative method for an inverse source problem of time-fractional diffusion-wave equation on spherically symmetric domain,” Journal of Applied Analysis and Computation, vol. 10, no. 2, pp. 1–16, April 2020.

    MathSciNet  Google Scholar 

  38. C. C. Yin and Y. Z. Wen, “An extension of Paulsen-Gjessing’s risk model with stochastic return on investments,” Insurance Mathematics & Economics, vol. 52, no. 3, pp. 469–476, May 2013.

    MathSciNet  MATH  Google Scholar 

  39. C. C. Yin, Y. Z. Wen, and Y. X. Zhao, “On the optimal dividend problem for a spectrally positive levy process,” Astin Bulletin, vol. 44, no. 3, pp. 635–651, September 2014.

    MathSciNet  MATH  Google Scholar 

  40. C. C. Yin and K. C. Yuen, “Exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory,” Frontiers of Mathematics in China, vol. 9, no. 6, pp. 1453–1471, December 2014.

    MathSciNet  MATH  Google Scholar 

  41. C. C. Yin and K. C. Yuen, “Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs,” Journal of Industrial and Management Optimization, vol. 11, no. 4, pp. 1247–1262, October 2015.

    MathSciNet  MATH  Google Scholar 

  42. S. S. Tian, X. X. Zhang, S. Xiao, J. Zhang, Q. Chen, and Y. Li, “Application of C6F12O/CO2 mixture in 10 kV medium-voltage switchgear,” IET Science Measurement & Technology, vol. 13, no. 9, pp. 1225–1230, November 2019.

    Google Scholar 

  43. G. Z. Zhang, X. X. Zhang, H. T. Cheng, and J. Tang, “Ladder-Wise calculation method for z-coordinate of transformer PD source based on planar layout UHF antenna sensors,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 15, no. 3, pp. 340–345, March 2020.

    Google Scholar 

  44. Y. Zhang, X. X. Zhang, Y. Li, Y. L. Li, Q. Chen, G. Z. Zhang, S. Xiao, and J. Tang, “AC breakdown and decomposition characteristics of environmental friendly gas C5F10O/Air and C5F10O/N-2,” IEEE Access, vol. 7, pp. 73954–73960, 2019.

    Google Scholar 

  45. Z. W. Chen, X. X. Zhang, H. Xiong, D. C. Chen, H. T. Cheng, J. Tang, Y. Tian, and S. Xiao, “Dissolved gas analysis in transformer oil using Pt-doped WSe2 monolayer based on first principles method,” IEEE Access, vol. 7, pp. 72012–72019, 2019.

    Google Scholar 

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

    MathSciNet  Google Scholar 

  47. Y. F. Chang, C. J. Sun, and Y. Qiu, “Effective notch stress method for fatigue assessment of sheet alloy material and bi-material welded joints,” Thin-Walled Structures, vol. 151, p. 106745, June 2020.

    Google Scholar 

  48. L. J. Wang, B. Y. Feng, Y. Wang, T. Z. Wu, and H. P. Lin, “Bidirectional short-circuit current blocker for DC microgrid based on solid-state circuit breaker,” Electronics, vol. 9, no. 2. p. 306, Febbruary 2020.

    Google Scholar 

  49. N. Zhao, “Joint optimization of cooperative spectrum sensing and Resource allocation in multi-channel cognitive radio sensor networks,” Circuits Systems and Signal Processing, vol. 35, no. 7, pp. 2563–2583, July 2016.

    MATH  Google Scholar 

  50. N. Zhao, M. H. Wu, and J. J. Chen, “Android-based mobile educational platform for speech signal processing,” International Journal of Electrical Engineering Education, vol. 54, no. 1, pp. 3–16, January 2017.

    Google Scholar 

  51. N. Zhao, Y. Liang, and Y. Pei, “Dynamic contract incentive mechanism for cooperative wireless networks,” IEEE Transactions on Vehicular Technology, vol. 67, no. 11, pp. 10970–10982, November 2018.

    Google Scholar 

  52. X. L. Zhao, F. Liu, B. Fu, and F. Na, “Reliability analysis of hybrid multi-carrier energy systems based on entropy-based Markov model,” Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability, vol. 230, no. 6, pp. 561–569, December 2016.

    Google Scholar 

  53. X. L. Zhao, Z. Y. Lin, B. Fu, L. He, and F. Na, “Research on automatic generation control with wind power participation based on predictive optimal 2-degree-of-freedom PID strategy for multi-area interconnected power system,” Energies, vol. 11, no. 12, Article Number: 3325, December 2018.

  54. L. Wang, H. Liu, L. V. Dai, and Y. W. Liu, “Novel method for identifying fault location of mixed lines,” Energies, vol. 11, no. 6, Article Number: 1529, June 2018.

  55. H. Liu, Q. X. Zou, Z. P. Zhang, “Energy disaggregation of appliances consumptions using ham approach,” IEEE Access, vol. 7, pp. 185977–185990, 2019.

    Google Scholar 

  56. X. S. Zhan, L. L. Cheng, J. Wu, and H. C. Yan, “Modified tracking performance limitation of networked time-delay systems with two-channel constraints,” Journal of the Franklin Institute, vol. 356, no. 12, pp. 6401–6418, August 2019.

    MathSciNet  MATH  Google Scholar 

  57. L. J. Wang, J. Guo, C. Xu, T. Z. Wu, and H. P. Lin, “Hybrid model predictive control strategy of supercapacitor energy storage system based on double active bridge,” Energies, vol. 12, no. 11, p. 2134, June 2019.

    Google Scholar 

  58. 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.

    MathSciNet  MATH  Google Scholar 

  59. 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, pp. 886–896, 2020.

    Google Scholar 

  60. W. X. Shi, N. Liu, Y. M. Zhou, X. A. Cao, “Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes,” IEEE Transactions on Electron Devices, vol. 66, no. 2, pp. 1057–1062, February 2019.

    Google Scholar 

  61. N. Liu, S. Mei, D. Sun, W. Shi, J. Feng, Y. M. Zhou, F. Mei, J. Xu, Y. Jiang, and X. A. Cao, “Effects of charge transport materials on blue fluorescent organic light-emitting diodes with a host-dopant system,” Micromachines, vol. 10, no. 5, Article Number: 344, May 2019.

  62. T. Z. Wu, X. Shi, L. Liao, C. J. Zhou, H. Zhou, and Y. H. Su, “A capacity configuration control strategy to alleviate power fluctuation of hybrid energy storage system based on improved particle swarm optimization,” Energies, vol. 12, no. 4, Article Number: 642, February 2019.

  63. X. L. Zhao, Z. Y. Lin, B. Fu, L. He, and C. S. Li, “Research on the predictive optimal PID plus second order derivative method for AGC of power system with high penetration of photovoltaic and wind power,” Journal of Electrical Engineering & Technology, vol. 14, no. 3, pp. 1075–1086, May 2019.

    Google Scholar 

  64. N. Li, S. Guo, and Y. Wang, “Weighted preliminary-summation-based principal component analysis for non-Gaussian processes,” Control Engineering Practice, vol. 87, pp. 122–132, June 2019.

    Google Scholar 

  65. 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.

  66. Z. D. Su, Y. Li, and G. C. Yang, “Dietary composition perception algorithm using social robot audition for Mandarin Chinese,” IEEE Access, vol. 8, pp. 8768–8782, 2020.

    Google Scholar 

  67. Y. F. Chang, G. S. Zhai, B. Fu, and L. L. Xiong, “Quadratic stabilization of switched uncertain linear systems: a convex combination approach,” IEEE-CAA Journal of Automatica Sinica, vol. 6, no. 5, pp. 1116–1126, September 2019.

    MathSciNet  Google Scholar 

  68. L. He, H. Lin, Q. Zou, and D. J. Zhang, “Accurate measurement of pavement deflection velocity under dynamic loads,” Automation in Construction, vol. 83, pp. 149–162, November 2017.

    Google Scholar 

  69. T. Z. Wu, F. C. Ye, Y. H. Su, Y. B. Wang, and S. Riffat, “Coordinated control strategy of DC microgrid with hybrid energy storage system to smooth power output fluctuation,” International Journal of Low-Carbon Technologies, vol. 15, no. 1, pp. 46–54, February 2020.

    Google Scholar 

  70. Y. Zhang, M. M. Huang, T. Z. Wu, and F. Ji, “Reconfigurable equilibrium circuit with additional power supply,” International Journal of Low-Carbon Technologies, vol. 15, no. 1, pp. 106–111, February 2020.

    Google Scholar 

  71. W. Wei, P. F. Xia, W. C. Xue, and M. Zuo, “On the disturbance rejection of a piezoelectric driven nanopositioning system,” IEEE Access, vol. 8, pp. 74771–74781, 2020.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, P. R. China

    Ling Xu & Feng Ding

  2. Department of Design, Manufacture and Engineering Management, Space Mechatronic Systems Technology Laboratory, Strathclyde Space Institute, University of Strathclyde, Glasgow, G1 1XJ, Scotland, UK

    Erfu Yang

Authors
  1. Ling Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erfu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ling Xu or Feng Ding.

Additional information

Recommended by Associate Editor M. Chadli under the direction of Editor Jay H. Lee.

This work was supported by the National Natural Science Foundation of China (No. 61873111) and the 111 Project (B12018).

Ling Xu was born in Tianjin, China. She received her Master’s and Ph.D. degrees from the Jiangnan University (Wuxi, China), in 2005 and 2015, respectively. She is a Post-Doctoral Fellow at the Jiangnan University and has been an Associate Professor since 2015. She is a Colleges and Universities “Blue Project” Young Teacher (Jiangsu, China). Her research interests include process control, parameter estimation and signal modeling.

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University, in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored four books on System Identification.

Erfu Yang received his B.Eng. and M.Eng. degrees both in Aerospace Propulsion Theory and Engineering from Beijing University of Aeronautics and Astronautics (Beijing, China) and a Ph.D. degree in Robotics from the School of Computer Science and Electronic Engineering at the University of Essex (Colchester, UK) in 2008. He is currently a Lecturer in the Department of Design, Manufacturing and Engineering Management (DMEM), the University of Strathclyde, Glasgow, UK. His main research interests include robotics, mechatronics, machine learning and artificial intelligence, etc. He has published more than 55 journal papers and 10 book chapters. Dr. Yang has been awarded over 15 research grants as PI (principal investigator) or CI (co-investigator). He is the Fellow of the UK Higher Education Academy, member of IEEE and IEEE Society of Robotics and Automation, committee member of the Chinese Automation and Computing Society in the UK (CACSUK), and the IET SCOTLAND Manufacturing Technical Network. He is also an associate editor for the Cognitive Computation journal published by Springer.

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, L., Ding, F. & Yang, E. Separable Recursive Gradient Algorithm for Dynamical Systems Based on the Impulse Response Signals. Int. J. Control Autom. Syst. 18, 3167–3177 (2020). https://doi.org/10.1007/s12555-019-0940-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0940-5

Keywords

Search

Navigation