Skip to main content

Comments on model validation as set membership identification

  • Part I Identification For Robust Control
  • Conference paper
  • First Online:
Robustness in identification and control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 245))

  • 102 Accesses

Abstract

We review four basic model validation techniques, one that relates to the “unknown-but-bounded” disturbance assumption, one that has been recently suggested in the “Identification-for-robust-control” context and two more classical statistical tests. By defining the set of models that would pass the chosen model validation test, we may interpret each of these as a set membership identification method. The consequences of such a viewpoint are discussed, and we focus on the important, but perhaps controversial concept of “independence” to make further selections of models within the thus defined sets.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.R. Deller. Set membership identification in digital signal processing. IEEE ASSP Magazine, 4:4–20, 1989.

    Article  Google Scholar 

  2. N.R. Draper and H. Smith. Applied Regression Analysis, 2nd ed. Wiley, New York, 1981.

    MATH  Google Scholar 

  3. R. Kosut, M. K. Lau, and S. P. Boyd. Set-membership identification of systems with parametric and nonparametric uncertainty. IEEE Trans. Automatic Control, AC-37:929–941, 1992.

    Article  MathSciNet  Google Scholar 

  4. L. Ljung. Identification, model validation and control. In Plenary Presentation at the 36th IEEE Conference on Decision and Control, San Diego, Dec 1997.

    Google Scholar 

  5. L. Ljung. Model validation and model error models. In Symposium, in Honor of Karl Johan Åström, To appear. Lund, Sweden, August 1999.

    Google Scholar 

  6. L. Ljung. System Identification — Theory for the User. 2nd edition, Prentice-Hall, Upper Saddle River, N.J., 1999.

    Google Scholar 

  7. L. Ljung and H. Hjalmarsson. System identification through the eyes of model validation. In Proc. Third European Control Conference, volume 3, Rome, Italy, Sep 1995.

    Google Scholar 

  8. P. M. Mäkilä, J. R. Partington, and T.K. Gustafsson. Worst-case control-relevant identification. Automatica, 31(12):1799–1819, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Ninness and G. C. Goodwin. Estimation of model quality. Automatica, 31(12):1771–1797, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Smith and J. C. Doyle. Model validation: a connection between robust control and identification. IEEE Trans. Automatic Control, AC-37:942–952, 1992.

    Article  MathSciNet  Google Scholar 

  11. R. Smith and G.E. Dullerud. Continuous-time control model validation using finite experimental data. IEEE Trans. Automatic Control, AC-41:1094–1105, 1996.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. Garulli (Assistant Professor)A. Tesi (Assistant Professor)

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag London Limited

About this paper

Cite this paper

Ljung, L. (1999). Comments on model validation as set membership identification. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109856

Download citation

  • DOI: https://doi.org/10.1007/BFb0109856

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-179-5

  • Online ISBN: 978-1-84628-538-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics