Skip to main content
SpringerLink
Log in

Newton iterative identification for a class of output nonlinear systems with moving average noises

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper discusses iterative identification problems for a class of output nonlinear systems (i.e., Wiener nonlinear systems) with moving average noises from input–output measurement data, based on the Newton iterative method. The basic idea is to decompose a nonlinear system into two subsystems, to replace the unknown variables in the information vectors with their corresponding estimates at the previous iteration, and to present a Newton iterative identification method using the hierarchical identification principle. The numerical simulation results indicate that the proposed algorithms are effective.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Ding, F.: System Identification—New Theory and Methods. Science Press, Beijing (2013)

    Google Scholar 

  2. Shi, Y., Yu, B.: Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668–1674 (2009)

    Article  MathSciNet  Google Scholar 

  3. Shi, Y., Yu, B.: Robust mixed H-2/H-infinity control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754–760 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Li, H., Shi, Y.: Robust H-infty filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains. Automatica 48(1), 159–166 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang, Q.J., Luo, J., Wan, L.: Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control. Nonlinear Dyn. 71(1–2), 353–359 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Qin, P., Nishii, R., Yang, Z.J.: Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods. Nonlinear Dyn. 70(3), 1831–1846 (2012)

    Article  MathSciNet  Google Scholar 

  7. Olson, C.C., Nichols, J.M., Virgin, L.N.: Parameter estimation for chaotic systems using a geometric approach: theory and experiment. Nonlinear Dyn. 70(1), 381–391 (2012)

    Article  MathSciNet  Google Scholar 

  8. Hizir, N.B., Phan, M.Q., Betti, R., Longman, R.W.: Identification of discrete-time bilinear systems through equivalent linear models. Nonlinear Dyn. 69(4), 2065–2078 (2012)

    Article  Google Scholar 

  9. Ding, F., Chen, T.: Identification of Hammerstein nonlinear ARMAX systems. Automatica 41(9), 1479–1489 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ding, F., Shi, Y., Chen, T.: Gradient-based identification methods for Hammerstein nonlinear ARMAX models. Nonlinear Dyn. 45(1–2), 31–43 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bai, E.W.: A blind approach to the Hammerstein–Wiener model identification. Automatica 38(6), 967–979 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, D.Q., Ding, F.: Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems. Comput. Math. Appl. 56(12), 3157–3164 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, D.Q., Ding, F.: Hierarchical least squares estimation algorithm for Hammerstein–Wiener systems. IEEE Signal Process. Lett. 19(12), 825–828 (2012)

    Article  Google Scholar 

  14. Wang, D.Q., Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011)

    Article  MATH  Google Scholar 

  15. Li, J.H., Ding, F.: Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique. Comput. Math. Appl. 62(11), 4170–4177 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, J.H., Ding, F., Yang, G.W.: Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 55(3–4), 442–450 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang, W., Ding, F., Dai, J.Y.: Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 36(5), 1842–1853 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dehghan, M., Hajarian, M.: An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices. Appl. Math. Model. 34(3), 639–654 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dehghan, M., Hajarian, M.: Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 35(7), 3285–3300 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wu, A.G., Li, B., Zhang, Y., Duan, G.R.: Finite iterative solutions to coupled Sylvester-conjugate matrix equations. Appl. Math. Model. 35(3), 1065–1080 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Liu, X.G., Lu, J.: Least squares based iterative identification for a class of multirate systems. Automatica 46(3), 549–554 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ding, F., Liu, Y.J., Bao, B.: Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng., Part I, J. Syst. Control Eng. 226(1), 43–55 (2012)

    Article  Google Scholar 

  23. Lorentzen, R.J., Naevdal, G.: An iterative ensemble Kalman filter. IEEE Trans. Autom. Control 56(8), 1990–1995 (2011)

    Article  MathSciNet  Google Scholar 

  24. Ding, F., Liu, X.P., Liu, G.: Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 20(3), 664–677 (2010)

    Article  Google Scholar 

  25. Wang, D.Q., Yang, G.W., Ding, R.F.: Gradient-based iterative parameter estimation for Box–Jenkins systems. Comput. Math. Appl. 60(5), 1200–1208 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Xie, L., Yang, H.Z.: Gradient based iterative identification for non-uniform sampling output error systems. J. Vib. Control 17(3), 471–478 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sun, Z., Zeng, J.P., Xu, H.R.: Generalized Newton-iterative method for semismooth equations. Numer. Algorithms 58(3), 333–349 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Arnal, J., Migallón, V., Penadés, J.: Parallel Newton two-stage multisplitting iterative methods for nonlinear systems. BIT Numer. Math. 43(5), 849–861 (2003)

    Article  MATH  Google Scholar 

  29. Xiong, W.L., Ma, J.X., Ding, R.F.: An iterative numerical algorithm for modeling a class of Wiener nonlinear systems. Appl. Math. Lett. 26(4), 487–493 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Liu, M.M., Xiao, Y.S., Ding, R.F.: Iterative identification algorithm for Wiener nonlinear systems using the Newton method. Appl. Math. Model. 37(9), 6584–6591 (2013)

    Article  MathSciNet  Google Scholar 

  31. Ding, F., Chen, T.: Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41(2), 315–325 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ding, F., Chen, T.: Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Autom. Control 50(3), 397–402 (2005)

    Article  MathSciNet  Google Scholar 

  33. Ding, F., Chen, T.: Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(6), 1179–1187 (2005)

    Article  MathSciNet  Google Scholar 

  34. Ding, J., Ding, F., Liu, X.P., Liu, G.: Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 56(11), 2677–2683 (2011)

    Article  MathSciNet  Google Scholar 

  35. Liu, Y.J., Ding, F., Shi, Y.: Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circuits Syst. Signal Process. 31(6), 1985–2000 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wang, D.Q., Ding, R., Dong, X.Z.: Iterative parameter estimation for a class of multivariable systems based on the hierarchical identification principle and the gradient search. Circuits Syst. Signal Process. 31(6), 2167–2177 (2012)

    Article  MathSciNet  Google Scholar 

  37. Ding, F., Shi, Y., Chen, T.: Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Syst. Control Lett. 56(5), 373–380 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Han, H.Q., Xie, L., Ding, F., Liu, X.: Hierarchical least squares based iterative identification for multivariable systems with moving average noises. Math. Comput. Model. 51(9–10), 1213–1220 (2010)

    Article  MATH  Google Scholar 

  39. Zhang, Z.N., Ding, F., Liu, X.G.: Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Comput. Math. Appl. 61(3), 672–682 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Ding, F.: Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694–1704 (2013)

    Article  MathSciNet  Google Scholar 

  41. Ding, F., Liu, X.P., Liu, G.: Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215–238 (2011)

    Article  Google Scholar 

  42. Ding, F., Liu, X.G., Chu, J.: Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 7(2), 176–184 (2013)

    Article  MathSciNet  Google Scholar 

  43. Zhang, Y.: Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods. Math. Comput. Model. 53(9–10), 1810–1819 (2011)

    Article  MATH  Google Scholar 

  44. Ding, F., Liu, G., Liu, X.P.: Parameter estimation with scarce measurements. Automatica 47(8), 1646–1655 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  45. Ding, F.: Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798–4808 (2013)

    Article  MathSciNet  Google Scholar 

  46. Liu, Y.J., Xiao, Y.S., Zhao, X.L.: Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477–1483 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  47. Liu, Y.J., Sheng, J., Ding, R.F.: Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615–2627 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  48. Ding, F.: Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7(1), 68–79 (2013)

    Article  MathSciNet  Google Scholar 

  49. Ding, F.: Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235–1242 (2013)

    Article  Google Scholar 

  50. Wang, D.Q.: Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648–1657 (2011)

    Article  MathSciNet  Google Scholar 

  51. Li, J.H., Ding, R.F., Yang, Y.: Iterative parameter identification methods for nonlinear functions. Appl. Math. Model. 36(6), 2739–2750 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  52. Ding, L., Han, L.L., Chen, X.M.: Time series AR modeling with missing observations based on the polynomial transformation. Math. Comput. Model. 51(5–6), 527–536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  53. Chen, J., Zhang, Y., Ding, R.F.: Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Math. Comput. Model. 52(9–10), 1428–1434 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  54. Chen, J., Wang, X.P., Ding, R.F.: Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities. Appl. Math. Model. 36(1), 238–243 (2012)

    Article  MATH  Google Scholar 

  55. Chen, J., Lv, L.X., Ding, R.F.: Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity. Appl. Math. Lett. 26(1), 124–129 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  56. Li, J.H.: Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91–96 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  57. Hu, P.P., Ding, F.: Multistage least squares based iterative estimation for feedback nonlinear systems with moving average noises using the hierarchical identification principle. Nonlinear Dyn. 73(1–2), 583–592 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61273194, 61203111), the Natural Science Foundation of Jiangsu Province (China, BK2012549), the Priority Academic Program Development of Jiangsu Higher Education Institutions and the 111 Project (B12018).

Author information

Authors and Affiliations

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

    Feng Ding, Junxia Ma & Yongsong Xiao

  2. Control Science and Engineering Research Center, Jiangnan University, Wuxi, 214122, P.R. China

    Feng Ding

Authors
  1. Feng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junxia Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yongsong Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng Ding.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, F., Ma, J. & Xiao, Y. Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn 74, 21–30 (2013). https://doi.org/10.1007/s11071-013-0943-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-013-0943-3

Keywords

Search

Navigation