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Identification of complex systems

  • Munther A. Dahleh
Part C Modeling, Identification And Estimation
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 241)

Abstract

In this paper, we discuss the problem of identifying a complex system with a limited-complexity model using finite corrupted data. Complex systems are ones that cannot be uniformly approximated by a finite dimensional space. Nevertheless, our prejudice is represented by selecting a finitely parameterized set of models from which an estimate of the original system will ultimately be drawn. We will give an account of a new formulation that shows how such a model should be selected from data. We will demonstrate this paradigm on the class of linear time-invariant stable systems and give an overview of the available results concerning input design, consistency, error bounds, and sample complexity.

Keywords

Finite Dimensional Subspace Unmodeled Dynamic Minimum Prediction Error White Noise Model White Noise Signal 
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.A. Dahleh, T. Theodosopoulos, and J.N. Tsitsiklis, “The sample complexity of worst-case identification of F.I.R. Linear systems,” System and Control. letters, Vol 20, No. 3, pp. 157–166, March 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    G.C. Goodwin, M. Gevers and B. Ninness, “Quantifying the error in estimated transfer functions with application to model order selection,” IEEE Trans. A-C, Vol 37, No. 7, July 1992.Google Scholar
  3. [3]
    G. Gu, P.P. Khargonekar and Y. Li, “Robust convergence of two stage nonlinear algorithms for identification in H , Systems and Control Letters, Vol 18, No. 4, April 1992.Google Scholar
  4. [4]
    A.J. Helmicki, C.A. Jacobson and C.N. Nett, “Control-oriented System Identification: A Worst-case/deterministic Approach in H ,” IEEE Trans. A-C, Vol 36, No. 10, October 1991.Google Scholar
  5. [5]
    M.K. Lau, R.L. Kosut, S. Boyd, “Parameter Set Estimation of Systems with Uncertain Nonparametric Dynamics and Disturbances”, Proceedings of the 29th Conference on Decision and Control, pp. 3162–3167, 1990.Google Scholar
  6. [6]
    M. Livstone and M.A. Dahleh. “A framework for robust parametric set membership identification,” IEEE Trans. A-C, vol 40, pp. 1934–1939, Nov 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    L. Lin, L. Wang and G. Zames, “Uncertainty principle and identification n-Widths for LTI and slowly varying systems,” ACC, Chicago, IL, 1992.Google Scholar
  8. [8]
    L. Ljung. System identification: theory for the user, Prentice-Hall, Inc, NJ, 1987.zbMATHGoogle Scholar
  9. [9]
    P.M. Makila, “Robust Identification and Galois Sequences”, Technical Report 91-1, Process Control Laboratory, Swedish University of Abo, January, 1991.Google Scholar
  10. [10]
    P.M. Makila and J.R. Partington, “Robust Approximation and Identification in H ”, Proc. 1991 American Control Conference, June, 1991.Google Scholar
  11. [11]
    M. Milanese and G. Belforte, “Estimation theory and uncertainty intervals evaluation in the presence of unknown but bounded errors: Linear families of models and estimators”, IEEE Trans. Automatic Control, AC-27, pp.408–414, 1982.CrossRefMathSciNetGoogle Scholar
  12. [12]
    M. Milanese and R. Tempo, “Optimal algorithm theory for robust estimation and prediction,” IEEE Trans. Automatic Control, AC-30, pp. 730–738, 1985.CrossRefMathSciNetGoogle Scholar
  13. [13]
    M. Milanese, ”Estimation theory and prediction in the presence of unknown and bounded uncertainty: a survey”, in Robustness in Identification and Control, M. Milanese, R. Tempo, A. Vicino Eds, Plenum Press, 1989.Google Scholar
  14. [14]
    J.P. Norton, “Identification and application of bounded-parameter models”, Automatica, vol.23, no.4, pp.497–507, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    K. Poolla and A. Tikku, “On the time complexity of worst-case system identification,” IEEE Trans. AC., May 1994.Google Scholar
  16. [16]
    F. C. Schweppe, “Uncertain Dynamical Systems”, Prentice Hall, Englewood Cliffs, NJ, 1973.Google Scholar
  17. [17]
    R. Smith and M. Dahleh. The Modeling of Uncertainty in Control Systems, Springer-Verlag, 1994.Google Scholar
  18. [18]
    D. Tse, M.A. Dahleh and J.N. Tsitsiklis. Optimal Asymptotic Identification under bounded disturbances. IEEE Trans. Automat. Contr., Vol.38, No. 8, pp. 1176–1190, August 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    S. Venkatesh. Identifcation for Complex Systems. MIT Ph.D thesis No. LIDS-Th-2394, July 1997.Google Scholar
  20. [20]
    S. Venkatesh and M.A. Dahleh, “Deterministic identification in the presence of unmodeled dynamics”, to appear in IEEE Trans. A-C. Dec 1997.Google Scholar
  21. [21]
    S. Venkatesh and M.A. Dahleh, “Identification of Complex systems with limited-complexity models,” Submitted to IEEE Trans. A-C.Google Scholar
  22. [22]
    S. Venkatesh, A. Megretski and M.A. Dahleh, “A convex parametrization of stabilizing controllers for perturbations belonging to a Hardy-Sobolev Space,” submitted.Google Scholar
  23. [23]
    G. Zames, “On the metric complexity of casual linear systems: ε-entropy and ε-dimension for continuous-time”, IEEE Trans. on Automatic Control, Vol. 24, April 1979.Google Scholar

Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Munther A. Dahleh
    • 1
  1. 1.Laboratory for Information and Decision SystemsMassachusetts Institute of TechnologyUSA

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