Advertisement

Two-stage Gradient-based Iterative Estimation Methods for Controlled Autoregressive Systems Using the Measurement Data

  • Feng DingEmail author
  • Lei Lv
  • Jian Pan
  • Xiangkui Wan
  • Xue-Bo Jin
Article
  • 6 Downloads

Abstract

This paper considers the parameter identification problems of controlled autoregressive systems using observation information. According to the hierarchical identification principle, we decompose the controlled autoregressive system into two subsystems by introducing two fictitious output variables. Then a two-stage gradient-based iterative algorithm is proposed by means of the iterative technique. In order to improve the performance of the tracking the time-varying parameters, we derive a two-stage multi-innovation gradient-based iterative algorithm based on the multi-innovation identification theory. Finally, an example is provided to illustrate the effectiveness of the proposed algorithms.

Keywords

Gradient search hierarchical identification iterative technique mathematical modeling multi-innovation identification parameter estimation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. [1]
    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,” Particle filtering based parameter estimation for systems with output-error type model structures, vol. 356, no. 10, pp. 5521–5540, July 2019.MathSciNetzbMATHGoogle Scholar
  2. [2]
    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,” Particle filtering-based recursive identification for controlled auto-regressive systems with quantised output, vol. 13, no. 14, pp. 2181–2187, 2019.Google Scholar
  3. [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,” A regularized variable projection algorithm for separable nonlinear least-squares problems, vol. 64, no. 2, pp. 526–537, February 2019.MathSciNetzbMATHGoogle Scholar
  4. [4]
    M. Gan, X. X. Chen, F. Ding, G. Y. Chen, and C. L. P. Chen, “Adaptive RBF-AR models based on multiinnovation least squares method,” Adaptive RBF-AR models based on multiinnovation least squares method, vol. 26, no. 8, pp. 1182–1186, August 2019.Google Scholar
  5. [5]
    L. Xu, “A proportional differential control method for a time-delay system using the Taylor expansion approximation,” Applied Mathematics and Computation, vol. 236, pp. 391–399, June 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    L. Xu, “Application of the Newton iteration algorithm to the parameter estimation for dynamical systems,” Journal of Computational and Applied Mathematics, vol. 288, pp. 33–43, November 2015.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    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,” Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration, vol. 79, no. 3, pp. 2155–2163, February 2015.MathSciNetGoogle Scholar
  8. [8]
    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.CrossRefGoogle Scholar
  9. [9]
    M. Gan, C. L. P. Chen, G. Y. Chen, and L. Chen, “On some separated algorithms for separable nonlinear squares problems,” On some separated algorithms for separable nonlinear squares problems, vol. 48, no. 10, pp. 2866–2874, October 2018.Google Scholar
  10. [10]
    L. Xu, “The parameter estimation algorithms based on the dynamical response measurement data,” The parameter estimation algorithms based on the dynamical response measurement data, vol. 9, no. 11, pp. 1–12, November 2017.Google Scholar
  11. [11]
    L. Xu, W. L. Xiong, A. Alsaedi, and T. Hayat, “Hierarchical parameter estimation for the frequency response based on the dynamical window data,” Hierarchical parameter estimation for the frequency response based on the dynamical window data, vol. 16, no. 4, pp. 1756–1764, August 2018.Google Scholar
  12. [12]
    S. Y. Liu, F. Ding, L. Xu, and T. Hayat, “Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals,” Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals, vol. 38, no. 7, pp. 3251–3268, July 2019.Google Scholar
  13. [13]
    H. Xu, F. Ding, and E. F. Yang, “Modeling a nonlinear process using the exponential autoregressive time series model,” Modeling a nonlinear process using the exponential autoregressive time series model, vol. 95, no. 3, pp. 2079–2092, February 2019.Google Scholar
  14. [14]
    J. J. Rubio, E. Lughofer, J. A. Meda-Campaña, L. A. Páramo, J. F. Novoa, and J. Pacheco, “Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models,” Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models, vol. 35, no. 2, pp. 2585–2596, August 2018.Google Scholar
  15. [15]
    Y. P. Pan, T. R. Sun, and H. Y. Yu, “On parameter convergence in least squares identification and adaptive control,” International Journal of Robust and Nonlinear Control, vol. 29, no. 10, pp 2898–2911, 2019.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    J. J. Rubio, “SOFMLS: Online self-organizing fuzzy modified least square network,” SOFMLS: Online self-organizing fuzzy modified least square network, vol. 17, no. 6, pp. 1296–1309, December 2009.Google Scholar
  17. [17]
    J. J. Rubio, “Stable Kalman filter and neural network for the chaotic systems identification,” Stable Kalman filter and neural network for the chaotic systems identification, vol. 354, no. 16, pp. 7444–7462, November 2017.MathSciNetzbMATHGoogle Scholar
  18. [18]
    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,” 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, vol. 33, no. 7, pp. 1189–1211, July 2019.MathSciNetzbMATHGoogle Scholar
  19. [19]
    M. H. Li and X. M. Liu, “Auxiliary model based least squares iterative algorithms for parameter estimation of bilinear systems using interval-varying measurements,” IEEE Access, vol. 6, pp. 21518–21529, January 2018.CrossRefGoogle Scholar
  20. [20]
    L. Xu, F. Ding, and Q. M. Zhu, “Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses,” Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses, vol. 50, no. 1, pp. 141–151, January 2019.MathSciNetGoogle Scholar
  21. [21]
    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.CrossRefGoogle Scholar
  22. [22]
    L. Xu and F. Ding, “The parameter estimation algorithms for dynamical response signals based on the multiinnovation theory and the hierarchical principle,” The parameter estimation algorithms for dynamical response signals based on the multiinnovation theory and the hierarchical principle, vol. 11, no. 2, pp. 228–237, April 2017.Google Scholar
  23. [23]
    L. Xu, F. Ding, Y. Gu, A. Alsaedi, and T. Hayat, “A multiinnovation state and parameter estimation algorithm for a state space system with d-step state-delay,” Signal Processing, vol. 140, pp. 97–103, November 2017.CrossRefGoogle Scholar
  24. [24]
    L. Xu and F. Ding, “Recursive least squares and multiinnovation stochastic gradient parameter estimation methods for signal modeling,” Recursive least squares and multiinnovation stochastic gradient parameter estimation methods for signal modeling, vol. 36, no. 4, pp. 1735–1753, April 2017.zbMATHGoogle Scholar
  25. [25]
    J. Chen, J. Li, and Y. J. Liu, “Gradient iterative algorithm for dual-rate nonlinear systems based on a novel particle filter,” Gradient iterative algorithm for dual-rate nonlinear systems based on a novel particle filter, vol. 354, no. 11, pp. 4425–4437, July 2017.MathSciNetzbMATHGoogle Scholar
  26. [26]
    L. Xu and F. Ding, “Iterative parameter estimation for signal models based on measured data,” Iterative parameter estimation for signal models based on measured data, vol. 37, no. 7, pp. 3046–3069, July 2018.MathSciNetzbMATHGoogle Scholar
  27. [27]
    F. Ding, System Identification — Iterative Search Principle and Identification Methods, Science Press, Beijing, 2018.Google Scholar
  28. [28]
    F. Ding, J. Pan, A. Alsaedi, and T. Hayat, “Gradient-based iterative parameter estimation algorithms for dynamical systems from observation data,” Mathematics, vol. 7, no. 5, Article Number: 428, May 2019.Google Scholar
  29. [29]
    Y. J. Wang, F. Ding, and M. H. Wu, “Recursive parameter estimation algorithm for multivariate output-error systems,” Recursive parameter estimation algorithm for multivariate output-error systems, vol. 355, no. 12, pp. 5163–5181, August 2018.MathSciNetzbMATHGoogle Scholar
  30. [30]
    H. Ma, J. Pan, L. Lv, G. H. Xu, F. Ding, A. Alsaedi, and T. Hayat, “Recursive algorithms for multivariable output-error-like ARMA systems,” Mathematics, vol. 7, no. 6, Article Number: 558, June 2019.Google Scholar
  31. [31]
    L. J. Wan and F. Ding, “Decomposition- and gradientbased iterative identification algorithms for multivariable systems using the multi-innovation theory,” Decomposition- and gradientbased iterative identification algorithms for multivariable systems using the multi-innovation theory, vol. 38, no. 7, pp. 2971–2991, July 2019.Google Scholar
  32. [32]
    Q. Y. Liu, F. Ding, L. Xu, and E. F. Yang, “Partially coupled gradient estimation algorithm for multivariable equationerror autoregressive moving average systems using the data filtering technique,” Partially coupled gradient estimation algorithm for multivariable equationerror autoregressive moving average systems using the data filtering technique, vol. 13, no. 5, pp. 642–650, March 2019.Google Scholar
  33. [33]
    X. Zhang, F. Ding, L. Xu, and E. F. Yang, “Highly computationally efficient state filter based on the delta operator,” Highly computationally efficient state filter based on the delta operator, vol. 33, no. 6, pp. 875–889, June 2019.MathSciNetzbMATHGoogle Scholar
  34. [34]
    X. Zhang, F. Ding, and E. F. Yang, “State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors,” State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors, vol. 33, no. 7, pp. 1157–1173, July 2019.MathSciNetzbMATHGoogle Scholar
  35. [35]
    F. Ding, F. F. Wang, L. Xu, T. Hayat, and A. Alsaedi, “Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique,” Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique, vol. 11, no. 3, pp. 390–400, February 2017.MathSciNetGoogle Scholar
  36. [36]
    F. Ding, L. Xu, F. E. Alsaadi, and T. Hayat, “Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique,” Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique, vol. 12, no. 7, pp. 892–899, May 2018.MathSciNetGoogle Scholar
  37. [37]
    L. Xu and F. Ding, “Parameter estimation for control systems based on impulse responses,” Parameter estimation for control systems based on impulse responses, vol. 15, no. 6, pp. 2471–2479, December 2017.Google Scholar
  38. [38]
    M. H. Wu, X. Li, C. Liu, M. Liu, N. Zhao, J. Wang, X. K. Wan, Z. H. Rao, and L. Zhu, “Robust global motion estimation for video security based on improved k-means clustering,” Robust global motion estimation for video security based on improved k-means clustering, vol. 10, no. 2, pp. 439–448, February 2019.Google Scholar
  39. [39]
    L. Feng, Q. X. Li, and Y. F. Li, “Imaging with 3-D aperture synthesis radiometers,” Imaging with 3-D aperture synthesis radiometers, vol. 57, no. 4, pp. 2395–2406, April 2019.Google Scholar
  40. [40]
    B. Fu, C. X. Ouyang, C. S. Li, J. W. Wang, and E. Gul, “An improved mixed integer linear programming approach based on symmetry diminishing for unit commitment of hybrid power system,” Energies, vol. 12, no. 5, Article Number: 833, March 2019.Google Scholar
  41. [41]
    W. X. Shi, N. Liu, Y. M. Zhou, and X. A. Cao, “Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes,” Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes, vol. 66, no. 2, pp. 1057–1062, February 2019.Google Scholar
  42. [42]
    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.Google Scholar
  43. [43]
    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.Google Scholar
  44. [44]
    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,” Research on the predictive optimal PID plus second order derivative method for AGC of power system with high penetration of photovoltaic and wind power, vol. 14, no. 3, pp. 1075–1086, May 2019.Google Scholar
  45. [45]
    X. S. Zhan, L. L. Cheng, J. Wu, Q. S. Yang, and T. Han, “Optimal modified performance of MIMO networked control systems with multi-parameter constraints,” Optimal modified performance of MIMO networked control systems with multi-parameter constraints, vol. 84, no. 1, pp. 111–117, January 2019.Google Scholar
  46. [46]
    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,” Modified tracking performance limitation of networked time-delay systems with two-channel constraints, vol. 356, no. 12, pp. 6401–6418, August 2019.MathSciNetzbMATHGoogle Scholar
  47. [47]
    X. D. Liu, H. S. Yu, J. P. Yu, and L. Zhao, “Combined speed and current terminal sliding mode control with nonlinear disturbance observer for PMSM drive,” IEEE Access, vol. 6, pp. 29594–29601, 2018.CrossRefGoogle Scholar
  48. [48]
    X. D. Liu, H. S. Yu, J. P. Yu, and Y. Zhao, “A novel speed control method based on port-controlled Hamiltonian and disturbance observer for PMSM drives,” IEEE Access, vol. 7, pp. 111115–111123, 2019.CrossRefGoogle Scholar
  49. [49]
    W. Wei, W. C. Xue, and D. H. Li, “On disturbance rejection in magnetic levitation,” Control Engineering Practice, vol. 82, pp. 24–35, January 2019.CrossRefGoogle Scholar
  50. [50]
    Z. Y. Sun, D. Zhang, Q. Meng, and C. C. Chen, “Feedback stabilization of time-delay nonlinear systems with continuous time-varying output function,” Feedback stabilization of time-delay nonlinear systems with continuous time-varying output function, vol. 50, no. 2, pp. 244–255, January 2019.Google Scholar
  51. [51]
    J. X. Ma, W. L. Xiong, J. Chen, and F. Ding, “Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter,” Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter, vol. 11, no. 6, pp. 857–869, April 2017.MathSciNetGoogle Scholar
  52. [52]
    F. Yang, Y. R. Sun, X. X. Li, and C. Y. Huang, “The quasiboundary value method for identifying the initial value of heat equation on a columnar symmetric domain,” The quasiboundary value method for identifying the initial value of heat equation on a columnar symmetric domain, vol. 82, no. 2, pp. 623–639, October 2019.zbMATHGoogle Scholar
  53. [53]
    F. Yang, N. Wang, X. X. Li, and C. Y. Huang, “A quasiboundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain,” Journal of Inverse and Ill-posed Problems, 2019. DOI: 10.1515/jiip-2018-0050Google Scholar
  54. [54]
    F. Yang, Y. Zhang, and X. X. Li, “Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation,” Numerical Algorithms, 2020. DOI: 10.1007/s11075-019-00734-6Google Scholar
  55. [55]
    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.CrossRefGoogle Scholar
  56. [56]
    N. Zhao, “Joint optimization of cooperative spectrum sensing and resource allocation in multi-channel cognitive radio sensor networks,” Joint optimization of cooperative spectrum sensing and resource allocation in multi-channel cognitive radio sensor networks, vol. 35, no. 7, pp. 2563–2583, July 2016.zbMATHGoogle Scholar
  57. [57]
    X. L. Zhao, F. Liu, B. Fu, and F. Na, “Reliability analysis of hybrid multi-carrier energy systems based on entropybased Markov model,” Reliability analysis of hybrid multi-carrier energy systems based on entropybased Markov model, vol. 230, no. 6, pp. 561–569, December 2016.Google Scholar
  58. [58]
    N. Zhao, M. H. Wu, and J. J. Chen, “Android-based mobile educational platform for speech signal processing,” Android-based mobile educational platform for speech signal processing, vol. 54, no. 1, pp. 3–16, January 2017.Google Scholar
  59. [59]
    J. Pan, X. Jiang, X. K. Wan, and W. Ding, “A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems,” A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems, vol. 15, no. 3, pp. 1189–1197, June 2017.Google Scholar
  60. [60]
    J. Pan, W. Li, and H. P. Zhang, “Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control,” Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control, vol. 16, no. 6, pp. 2878–2887, December 2018.Google Scholar
  61. [61]
    P. C. Gong, W. Q. Wang, and X. R. Wan, “Adaptive weight matrix design and parameter estimation via sparse modeling for MIMO radar,” Signal Processing, vol. 139, pp. 1–11, October 2017.CrossRefGoogle Scholar
  62. [62]
    P. C. Gong, W. Q. Wang, F. C. Li, and H. Cheung, “Sparsity-aware transmit beamspace design for FDAMIMO radar,” Signal Processing, vol. 144, pp. 99–103, March 2018.CrossRefGoogle Scholar
  63. [63]
    N. Zhao, Y. Liang, and Y. Pei, “Dynamic contract incentive mechanism for cooperative wireless networks,” Dynamic contract incentive mechanism for cooperative wireless networks, vol. 67, no. 11, pp. 10970–10982, November 2018.Google Scholar
  64. [64]
    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.Google Scholar
  65. [65]
    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: 1520, June 2018.Google Scholar
  66. [66]
    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,” Filtering-based multistage recursive identification algorithm for an input nonlinear output-error autoregressive system by using key the term separation technique, vol. 36, no. 2, pp. 577–599, February 2017.zbMATHGoogle Scholar
  67. [67]
    P. Ma and F. Ding, “New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering,” New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering, vol. 354, no. 3, pp. 1568–1583, February 2017.MathSciNetzbMATHGoogle Scholar
  68. [68]
    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,” Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering, vol. 354, no. 3, pp. 1321–1339, February 2017.MathSciNetzbMATHGoogle Scholar
  69. [69]
    H. Ma, J. Pan, F. Ding, L. Xu, and W. Ding, “Partiallycoupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems,” IET Control Theory and Applications, vol. 13, 2019. DOI: 10.1049/iet-cta.2019.0112Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.Hubei Key Laboratory for High-efficiency Utilization of Solar Energy and Operation Control of Energy Storage System, the School of Electrical and Electronic EngineeringHubei University of TechnologyWuhanP. R. China
  2. 2.College of Automation and Electronic EngineeringQingdao University of Science and TechnologyQingdaoP. R. China
  3. 3.School of Computer and Information EngineeringBeijing Technology and Business UniversityBeijingP. R. China

Personalised recommendations