Skip to main content
SpringerLink
Log in

Iterative selection of GOB poles in the context of system modeling

  • Research Article
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

This paper is concerned with the problem of system identification using expansions on generalized orthonormal bases (GOB). Three algorithms are proposed to optimize the poles of such a basis. The first two algorithms determine a GOB with optimal real poles while the third one determines a GOB with optimal real and complex poles. These algorithms are based on the estimation of the dominant mode associated with a residual signal obtained by iteratively filtering the output of the process to be modelled. These algorithms are iterative and based on the quadratic error between the linear process output and the GOB based model output. They present the advantage to be very simple to implement. No numerical optimization technique is needed, and in consequence there is no problem of local minima as is the case for other algorithms in the literature. The convergence of the proposed algorithms is proved by demonstrating that the modeling quadratic error between the process output and the GOB based model is decreasing at each iteration of the algorithm. The performance of the proposed pole selection algorithms are based on the quadratic error criteria and illustrated by means of simulation results.

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. B. Wahlberg. System identification using Laguerre models, IEEE Transactions on Automatic Control, vol. 36, no. 5, pp. 551–562, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Wahlberg. System identification using Kautz models, IEEE Transactions on Automatic Control, vol. 39, no. 6, pp. 1276–1282, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  3. K. Bouzrara, T. Garna, J. Ragot, H. Messaoud. Decomposition of an ARX model on Laguerre orthonormal bases, ISA Transactions, vol. 51, no. 6, pp. 848–860, 2012.

    Article  MATH  Google Scholar 

  4. N. Saidi, H. Messaoud. Supervised equalization of a linear communication channel using generalized orthogonal basis (GOB), In Proceedings of the 6th International Multi-Conference on Systems, Signals and Devices, Jerba, Tunisia, 2009.

    Google Scholar 

  5. P. S. C. Heuberger. P. M. J. Van den Hof, O. H. Bosgra, A generalized orthonormal basis for linear dynamical systems, IEEE Transactions on Automatic Control, vol. 40, no. 3, pp. 451–465, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Bouzrara, T. Garna, J. Ragot and H. Messaoud, Decomposition of an ARX model on Laguerre orthonormal bases. ISA Transactions, vol. 51, no. 6, pp. 848–860, 2012

    Article  MATH  Google Scholar 

  7. A. C. den Brinker, H. J. Belt. Model reduction by orthogonalized exponential sequences. In Proceedings of PRORIS/IEEE Workshop on Circuits, System and Signal Processing, Mierlo, Netherlands, pp. 77–82, 1996.

    Google Scholar 

  8. R. Malti, D. Maquin, J. Ragot. Optimality conditions for the truncated network of the generalized discrete orthonormal basis having real poles, In Proceedings of IEEE Conference on Decision and Control, Tampa, Florida, USA, pp. 2189–2194, 1998.

    Google Scholar 

  9. A. Kibangou, G. Favier, M. M. Hassani. A growing approach for selecting generalized orthonormal basis functions in the context of system modeling, In Proceedings of IEEEEURASIP Workshop on Nonlinear Signal and Image Processing, IEEE, Grado, Italy, 2003.

    Google Scholar 

  10. A. Mbarek, K. Bouzrara, H. Messaoud, Optimal expansion of linear system using generalized orthogonal basis. In Proceedings of International Conference on Electrical Engineering and Software Applications, Hammamet, Tunisia, 2013

    Google Scholar 

  11. A. da Rosa, R.J.G.B. Campello, W.C. Amaral. An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension, International Journal of Control, vol. 81, no. 6, pp. 962–975, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Garna, K. Bouzrara, J. Ragot, H. Messaoud. Nonlinear system modeling based on bilinear Laguerre orthonormal bases, ISA Transactions, vol. 51, no. 6, pp. 848–860, 2012

    Article  MATH  Google Scholar 

  13. A. Kibangou, G. Favier, M. M. Hassani. Iterative optimization method of GOB-volterra filters. In Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, vol. 38, no. 1, pp. 773–778, 2005.

    Google Scholar 

  14. A. Kibangou, G. Favier, M. M. Hassani. Selection of generalized orthonormal bases for second-order Volterra filters, Signal Processing, vol. 85, no. 12, pp. 2371–2385, 2005.

    Article  MATH  Google Scholar 

  15. A. da Rosa et al. Robust expansion of uncertain Volterra kernels into orthonormal series, In Proceedings of the American Control Conference, Marriott Waterfront, Baltimore, MD, USA, pp. 5465–5470, 2010.

    Google Scholar 

  16. A. da Rosa, R. J. G. B. Campello, W. C. Amaral. Exact search directions for optimization of linear and nonlinear models based on generalized orthonormal functions. IEEE Transactions on Automatic Control, vol. 54, no. 12, pp. 2757–2772, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Mathlouthi, K. Abederrahim, F. Msahli and G. Favier. Crosscumulants based approaches for the structure identification of Volterra models, International Journal of Automation and Computing, vol. 6, no. 4, pp. 420–430, 2009.

    Article  Google Scholar 

  18. M. Ltaief, A. Messaoud and R. Ben Abdennour. Optimal systematic determination of models base for multimodel representation: real time application, International Journal of Automation and Computing, vol. 11, no. 6, pp. 644–652, 2014.

    Article  Google Scholar 

  19. B. Ninness, F. Gustafsson. A unifying construction of orthonormal bases for system identification, IEEE Transactions on Automatic Control, vol. 42, no. 4, pp. 515–521, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  20. G. A. Dumont, Y. Fu, Non-linear adaptive control via Laguerre expansion of Volterra kernels. Int. J. Adaptive Control and Signal Processing, vol. 7, pp. 367–382, 1993.

    Article  MATH  Google Scholar 

  21. Y. Fu, G. A. Dumont. An optimum time scale for discrete Laguerre network. IEEE Transactions on Automatic Control, vol. 38, no. 6, pp. 934–938, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  22. N. Tanguy, R. Morvan, P. Vilb, C. Calvez. Online optimization of the time scale in adaptive Laguerre based filters, IEEE Transactions on Signal Processing, vol. 48, no. 4, pp. 1184–1187, 2002.

    Article  Google Scholar 

  23. M. Guglielmi. Signaux Aleatoires, Modelisation, Estimation, Detection. Paris, France: Editions Hermes Science, 2004.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. High Institute of Applied Science and Technology, Sousse, 4003, Tunisia

    Anis Khouaja

  2. National Engineering School of Monastir (ENIM), Monastir, 5019, Tunisia

    Anis Khouaja & Hassani Messaoud

Authors
  1. Anis Khouaja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassani Messaoud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anis Khouaja.

Additional information

Recommended by Editor-in-Chief Guoping Liu

Anis Khouaja recieved the B.Eng. degree from the National Engineering School of Monastir (ENIM), Tunisia in 2000. He received the M. Sc. and Ph.D. degrees from the University of Nice Sophia Antipolis, France in 2001 and 2005, respectively. Currently, he is an assistant professor in Electrical Engineering Department, High Institute of Applied Science and Technology of Sousse, Tunisia. He is also with the LARATSI Laboratory of the Engineering National School of Monastir in Tunisia.

His research interests include system modeling and identification, nonlinear system theory and robust predictive control.

Hassani Messaoud is a full professor with the Electrical Engineering Department of the National School of Engineers of Monastir, Tunisia. He is also the head of the LARATSI Laboratory in the same school.

His research interests include system modeling and identification, nonlinear system theory, robust predictive control, diagnostic and digital channel equalization.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khouaja, A., Messaoud, H. Iterative selection of GOB poles in the context of system modeling. Int. J. Autom. Comput. 16, 102–111 (2019). https://doi.org/10.1007/s11633-016-0984-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-016-0984-4

Keywords

Search

Navigation