Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling

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

Abstract

This paper focuses on the identification problem of Wiener nonlinear systems with non-uniform sampling. The mathematical model for the Wiener nonlinear system is established from the non-uniformly sampled input–output data. In order to solve the identification problem of the Wiener nonlinear system with the unmeasurable variables in the information vector, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. Finally, the simulation results indicate that the proposed algorithm is effective.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Shaker, H.R., Stoustrup, J.: An interaction measure for control configuration selection for multivariable bilinear systems. Nonlinear Dyn. 72(1–2), 165–174 (2013)

    Article  MathSciNet  Google Scholar 

  2. Janczak, A.: Instrumental variables approach to identification of a class of MIMO Wiener systems. Nonlinear Dyn. 48(3), 275–284 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, J., Zhang, Y., et al.: Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model. Nonlinear Dyn. 72(4), 865–871 (2013)

    Article  MATH  Google Scholar 

  4. 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  MATH  MathSciNet  Google Scholar 

  5. Ding, F., Chen, T.: Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ding, F., Liu, P.X., 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 

  7. 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  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  9. Dehghan, M., Hajarian, M.: An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation. Appl. Math. Comput. 202(2), 571–588 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dehghan, M., Hajarian, M.: Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A 1 X 1 B 1+A 2 X 2 B 2=C. Math. Comput. Model. 49(9–10), 1937–1959 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dehghan, M., Hajarian, M.: Iterative algorithms for the generalized centrosymmetric and central anti-symmetric solutions of general coupled matrix equations. Eng. Comput. 29(5), 528–560 (2012)

    Article  Google Scholar 

  12. Zhou, L.C., Li, X.L., Pan, F.: Gradient based iterative parameter identification for Wiener nonlinear systems. Appl. Math. Model. 37(16–17), 8203–8209 (2013)

    Article  MathSciNet  Google Scholar 

  13. Zhou, L.C., Li, X.L., Pan, F.: Gradient-based iterative identification for MISO Wiener nonlinear systems: application to a glutamate fermentation process. Appl. Math. Lett. 26(8), 886–892 (2013)

    Article  MathSciNet  Google Scholar 

  14. Ding, F., Ma, J.X., Xiao, Y.S.: Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn. 74(1–2), 21–30 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Shafiee, G., Arefi, M., et al.: Nonlinear predictive control of a polymerization reactor based on piecewise linear Wiener model. Chem. Eng. J. 143(1), 282–292 (2008)

    Article  Google Scholar 

  16. da Silva, M.M., Wigren, T., Mendonça, T.: Nonlinear identification of a minimal neuromuscular blockade model in anesthesia. IEEE Trans. Control Syst. Technol. 20(1), 181–188 (2012)

    Google Scholar 

  17. Chen, J.: Gradient based iterative algorithm for Wiener systems with piecewise nonlinearities using analytic parameterization methods. Comput. Appl. Chem. 28(7), 855–857 (2011)

    Google Scholar 

  18. 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 

  19. Pelckmans, K.: MINLIP for the identification of monotone Wiener systems. Automatica 47(10), 2298–2305 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  20. Shi, Y., Ding, F., Chen, T.: Multirate crosstalk identification in xDSL systems. IEEE Trans. Commun. 54(10), 1878–1886 (2006)

    Article  Google Scholar 

  21. Yu, B., Shi, Y., Huang, H.: L-2 and L-infinity filtering for multirate systems using lifted models. Circuits Syst. Signal Process. 27(5), 699–711 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  22. Shi, Y., Fang, H.: Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538–551 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  23. 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  MATH  MathSciNet  Google Scholar 

  24. Ding, F., Liu, G., Liu, X.P.: Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Autom. Control 55(8), 1976–1981 (2010)

    Article  MathSciNet  Google Scholar 

  25. Ding, F., Qiu, L., Chen, T.: Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 45(2), 324–332 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. Xie, L., Yang, H.Z., et al.: Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering. Math. Comput. Model. 54(1–2), 315–324 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  27. Han, L.L., Sheng, J., et al.: Auxiliary models based recursive least squares identification for multirate multi-input systems. Math. Comput. Model. 50(7–8), 1100–1106 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Vörös, J.: Modeling and identification of systems with backlash. Automatica 46(2), 369–374 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  29. Han, L.L., Ding, F.: Parameter estimation for multirate multi-input systems using auxiliary model and multi-innovation. J. Syst. Eng. Electron. 21(6), 1079–1083 (2010)

    Google Scholar 

  30. 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 

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

    Article  Google Scholar 

  32. Ding, F.: Combined state and least squares parameter estimation algorithms for dynamic systems. Appl. Math. Model. 38(1), 403–412 (2014)

    Article  MathSciNet  Google Scholar 

  33. Ding, F., Liu, X.M., Chen, H.B., Yao, G.Y.: Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems. Signal Process. 97, 31–39 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61273131), the Fundamental Research Funds for the Central Universities (JUDCF11042, JUDCF12031), and the PAPD of Jiangsu Higher Education Institutions and the 111 Project (B12018).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lincheng Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, L., Li, X. & Pan, F. Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling. Nonlinear Dyn 76, 627–634 (2014). https://doi.org/10.1007/s11071-013-1156-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-013-1156-5

Keywords

Navigation