Model Quality for the Windsurfer Scheme of Adaptive Control

  • Robert R. Bitmead
  • Wayne J. Dunstan


The Windsurfer Approach to adaptive control combines Internal Model Control (IMC) design parametrized by the desired closed-loop bandwidth with event-driven system identification using Hansen’s scheme on closed-loop data. Our aim in this work is to investigate the nature of model quality applicable to the windsurfer approach. We do this by expanding on recent activities dealing with the complete class of all models suited to model reference control design. In particular, we interpret the conditions for simultaneous stabilization of the plant and the model by an IMC controller. This extends the model reference results to a different domain in which the controller is characterized algebraically by the model but also inherently includes a specification of design performance objective.


Internal Model Control Adaptive Robust Control Complete Class Complementary Sensitivity Unstable Zero 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lee, W. S., Anderson, B. D. O. Kosut, R. L., Mareels, I M. Y. (1993) “A new approach to adaptive robust control”, International Journal of Adaptive Control and Signal Processing, vol. 7, pp. 183–211.MATHCrossRefGoogle Scholar
  2. 2.
    Lee, W.S., Anderson, B. D. O., Mareels, I. M. Y., Kosut, R. L. (1995) “On some key issues in the windsurfer approach to adaptive robust control”Automatica, vol. 31, pp. 1619–1636.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Morari, M., Zafiriou, E. (1989) Robust Process Control, Prentice-Hall, NJ.Google Scholar
  4. 4.
    Hansen, F., Franklin, G. F., Kosut, R. L. (1989) “Closed loop identification via the fractional representation”, Proc. 1989 American Control Conference, Pittsburgh PA.Google Scholar
  5. 5.
    Liu, K., Skelton, R. E. (1990) “Closed-loop identification and iterative controller design”, Proc. 29th IEEE Conference on Decision and Control, Honolulu HI, pp. 482–487.Google Scholar
  6. 6.
    Hakvoort, R. G., Schrama, R. J. P., Van den Hof, P. M. J. (1994) “Approximate identification with closed-loop performance criterion and application in LQG feedback design”, Automatical vol. 30, pp. 679–690.MATHCrossRefGoogle Scholar
  7. 7.
    Schrama, R. J. P., Bosgra, O. H. (1993) “Adaptive performance enhancement by iterative identification and control design”, International Journal of Adaptive Control and Signal Processing, vol. 7, pp. 475–487.MATHCrossRefGoogle Scholar
  8. 8.
    Van den Hof, P. M. J., Schrama, R. J. P. (1993) “An indirect method for transfer function estimation from closed-loop data”, Automatica, vol. 29, pp. 1523–1527.MATHCrossRefGoogle Scholar
  9. 9.
    Zang, Z., Bitmead, R. R., Gevers, M. (1995) “Iterative weighted Least Squares identification and weighted LQG Control Design”, Automatica, vol 31, No 11, pp. 1577–1594.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Gevers, M., Bitmead, R. R., Blondel, V. (1997) “Unstable ones in understood algebraic problems of modelling for control design”, Mathematical Modelling of Systems, vol. 3, pp. 59–76.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Blondel, V., Gevers, M., Bitmead, R. R. (1997) “When is a model good for control design”, IEEE Conference on Decision and Control, San Diego, CA, pp. 1283–1288.Google Scholar
  12. 12.
    Gevers, M. (1993) “Towards a joint design of identification and control?”, In H.L. Trentelman and J.C. Willems (Eds), Essays on Control: Perspectives in the Theory and its Applications, pp. 111–151. Birkhauser, Boston.Google Scholar
  13. 13.
    Liu, Y., Anderson, B. D. O. (1986) “Controller reduction via stable factorization and balancing”, International Journal of Control, vol. 44, pp. 507–531.MATHCrossRefGoogle Scholar
  14. 14.
    Woertelboer, P. M. R. (1994) Frequency-weighted balanced reduction of closed- loop mechanical servo-systems: theory and tools, PhD Thesis, Mechanical Engi¬neering Department, Delft Technical University, The Netherlands.Google Scholar
  15. 15.
    Ng, T. S., Goodwin, G. C., Anderson, B. D. O. (1977) “On the identifiability of multiple-input multiple-output linear dynamic systems operating in closed loop”, Automatica, Vol 13, pp 477–486.MATHCrossRefGoogle Scholar
  16. 16.
    Anderson, B. D. O., Gevers, M.R. (1982) “Identifiability of linear stochastic systems operating under linear feedback”, Automatica, Vol 18, pp 195–214.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Dasgupta, S., Anderson, B. D. O. (1996) “A parametrization for the closed- loop identification of nonlinear time-varying systems”, Automatica, Vol 32, No 10, pp 1349–1360.MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    DeBruyne, F., Anderson, B. D. O. Gevers, M., Linard, N. (1999) “Gradient ex-pressions for a closed-loop identification scheme with a tailor-made parametriza- tion”, Automatica, Vol 35, pp 1867–1871.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Linard, N., Anderson, B. D. O., De Bruyne, F. (1999) “Identification of a nonlinear plant under nonlinear feedback using left coprime fractional based representation”, Automatica, Vol 35, pp 655–667.MATHCrossRefGoogle Scholar
  20. 20.
    Codrons, B., Anderson, B. D. O., Gevers, M. (2000) “Closed-loop identification with an unstable or nonminimum phase controller” IFAC Symposium on System Identification, Santa Barbara CA.Google Scholar
  21. 21.
    Liu, Y, Anderson, B. D. O. (1989) “Singular perturbation approximation of balanced systems”, International Journal of Control Vol 50, pp 1379–1405.MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Anderson, B. D. O., Liu, Y, (1989) “Controller reduction; concepts and ap-proaches”, IEEE Trans. on Automatic Control, Vol 34, pp 802–812.MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Liu, Y., Anderson, B. D. O., Ly, U-L. (1990) “Coprime factorization controller reductions with Bezout identity induced frequency weighting”, Automatica, Vol 26, pp 233–249.MathSciNetMATHGoogle Scholar
  24. 24.
    Madievski, A. G., Anderson, B. D. O. (1995) “Sampled-Data controller reduc-tion procedure”, IEEE Trans on Auto. Control, Vol 40, pp 1922–1926.MathSciNetMATHGoogle Scholar
  25. 25.
    Anderson, B. D. O., Kosut, E. L. (1991) “Adaptive robust control: on-line learning”, Proc IEEE 30th Conf on Decision and Control, Brighton UK, pp 297–298.Google Scholar
  26. 26.
    Anderson, B. D. O. (1998) “From Youla-Kucera to identification, adaptive and nonlinear control”, Automatica, Vol 34, pp 1485–1506.MATHCrossRefGoogle Scholar
  27. 27.
    A.C. Antoulas, A. C., Anderson, B. D. O. (1999) “On the choice of inputs in identification for robust control”, Automatica, vol 35, pp 1009–1031.MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Anderson, B. D. O. (1992) “Optimizing the Discretization of Continuous-Time Controllers”, Recent Advances in Mathematical Theory of Systems Control Net-works & Signal Processing I, H. Kimura and S. Kodema (eds), Mita Press, pp 475–480.Google Scholar
  29. 29.
    Keller, J. P., Anderson, B. D. O. (1992) “A new approach to the discretization of continuous-time controllers” IEEE Trans Auto Control, vol 37, pp 214–223.MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Anderson, B. D. 0., Bombois, X., Gevers, M., Kulcsar, K. (1998) “Caution in iterative modeling and control design” IFAC Workshop on Adaptive Systems in Control and Signal Processing, University of Strathclyde, Glasgow, pp 13–19.Google Scholar
  31. 31.
    Anderson, B. D. O., Gevers, M. (1998) “Fundamental problems in adaptive control”, Perspectives in Control, D. Normand-Cyrot (ed.), Springer, Berlin, pp 9–21.Google Scholar

Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Robert R. Bitmead
    • 1
  • Wayne J. Dunstan
    • 1
  1. 1.University of California San DiegoUSA

Personalised recommendations