Worst-Case l1 Identification

  • M. Milanese

Abstract

In this chapter recent results on nonparametric and mixed parametric-nonparametric l 1 identification are reviewed. These results mainly concern the evaluation of the identification errors, the design of experiment, the selection of the model structure, the construction of optimal and almost optimal algorithms, and the convergence properties of the identification algorithms.

Keywords

Impulse Response Identification Procedure Nonparametric Approach Projection Algorithm Identification Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    M. Milanese and A. Vicino, Automatica 27, 997 (1991).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    E. Walter and H. Piet-Lahanier, Math. Comp. Sim. 32, 499 (1990).Google Scholar
  3. 3.
    A. B. Kurzhanski, Control and Observation under Conditions of Uncertainty, Nauka, Moscow, Russia (1977).Google Scholar
  4. 4.
    V. M. Kuntzevich and M. Lychak, Guaranteed Estimates, Adaptation and Robustness in Control Systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin, Germany (1992).MATHCrossRefGoogle Scholar
  5. 5.
    M. Milanese and A. Vicino, J. Complex. 9, 427 (1993).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    G. C. Goodwin, M. Gevers, and B. Ninness, IEEE Trans. Autom. Control 37, 913 (1992).MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    B. Wahlberg and L. Ljung, IEEE Trans. Autom. Control 37, 900 (1992).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    R. L. Kosut, M. K. Lau, and S. P. Boyd, IEEE Trans. Autom. Control 37, 929 (1992).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    N. Elia and M. Milanese, in: Proceedings of the 32nd IEEE CDC, San Antonio, Texas, pp. 545-550 (1993).Google Scholar
  10. 10.
    M. A. Dahleh and J. B. Pearson, IEEE Trans. Autom. Control 32, 314 (1987).MATHCrossRefGoogle Scholar
  11. 11.
    C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York (1975).MATHGoogle Scholar
  12. 12.
    J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski, Information-Based Complexity, Academic Press, New York (1988).MATHGoogle Scholar
  13. 13.
    P. M. Makila and J. R. Partington, in: Proceedings of the 1991 ACC, pp. 70-76 (1991).Google Scholar
  14. 14.
    L. Lin, L. Y Wang, and G. Zames, in: Proceedings of the ACC 1992, pp. 296-300 (1992).Google Scholar
  15. 15.
    A. Pinkus, n-Widths in Approximation Theory, Springer-Verlag, Berlin, Germany (1985).MATHCrossRefGoogle Scholar
  16. 16.
    B. Kacewicz and M. Milanese, in: Proceedings of the IEEE 31 st Control and Decision Conference, Tucson, AZ, pp. 56-61 (1992).Google Scholar
  17. 17.
    B. Kacewicz and M. Milanese, Jour. Adapt. Contr. Signal Process 9, 87–96 (1994).MathSciNetCrossRefGoogle Scholar
  18. 18.
    J. Chen, C. N. Nett, and M. K. Fan, in: Proceedings of the 1992 American Control Conference, pp. 279-286, Chicago, IL (1992).Google Scholar
  19. 19.
    M. Milanese and B. Kacewicz, in: IIASA 1992 Workshop on Modeling Techniques for Uncertain Systems (Kurzhansky and Veliov, eds.), Birkhauser, Boston, MA (1994).Google Scholar
  20. 20.
    M. A. Dahleh, T. Theodosopoulos, and J. N. Tsitsiklis, in: Proceedings of the 32nd IEEE CDC, San Antonio, Texas (1993).Google Scholar
  21. 21.
    K. Poolla and A. Tikku, Proceedings of the 1993 ACC, San Francisco, pp. 141-145 (1993).Google Scholar
  22. 22.
    M. Milanese, Proceedings of IFAC-SYSID’94, Copenhagen (1994), also Automatica 31, 327 (1995).MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    N. Dunford and J. T. Schwarz, Linear Operators, vol. 1, Interscience, New York (1958).MATHGoogle Scholar
  24. 24.
    M. Milanese and R. Tempo, IEEE Trans. Autom. Control 30, 730 (1985).MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    K. Trustrum, Linear Programming, Chap. 2, Routledge and Kegan Paul, London (1971).MATHCrossRefGoogle Scholar
  26. 26.
    T. H. Matheiss and D. S. Rubin, Math. Oper. Res. 5, 167 (1980).MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    S. H. Mo and J. P. Norton, Math. Conput. Simul. 32, 481 (1990).MathSciNetCrossRefGoogle Scholar
  28. 28.
    A. Vicino and M. Milanese, IEEE Trans. Autom. Control 36, 759 (1991).MathSciNetCrossRefGoogle Scholar
  29. 29.
    M. L. Overton, in: Nonlinear Optimization 1981 (M. J. D. Powell, ed.), Academic Press, New York (1982).Google Scholar
  30. 30.
    B. Z. Kacewicz, M. Milanese, R. Tempo, and A. Vicino, Syst. Control Lett. 8, 161 (1986).MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    P. M. Mäkä, International J. Control 54, 1189 (1991).CrossRefGoogle Scholar
  32. 32.
    D. C. N. Tse, M. A. Dahleh, and J. N. Tsitsiklis, in: Control of Uncertain Dynamic Systems (S. P. Bhattacharyya and L. H. Keel, eds.), CFC Press, pp. 311-328 (1991).Google Scholar
  33. 33.
    C. A. Jacobson and C. N. Nett, in: Proceedings of the 1991 American Control Conference, Boston (1991).Google Scholar
  34. 34.
    P. M. Makila and J. R. Partington, in: Proceedings of the 1992 American Control Conference, pp. 301-306, Chicago (1992).Google Scholar
  35. 35.
    L. Ljung, System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, NJ (1987).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • M. Milanese
    • 1
  1. 1.Dipartimento di Automatica e InformaticaPolitecnico di TorinoTorinoItaly

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