Advertisement

Finite-Data Algorithms for Approximate Stochastic Realization

  • Richard J. Vaccaro

Abstract

This chapter deals with the problem of constructing a state-space model for a stochastic process from a finite number of estimated covariance lags. The approach is to first obtain a high-order model which exactly matches the estimated covariance sequence, and then use balanced model reduction techniques to obtain a lower order model which approximates the given sequence. It is shown that balanced models can be obtained from a realization algorithm which uses an infinite covariance sequence. Scaling ideas are then introduced so that balanced realizations can be obtained from finite covariance sequences.

Keywords

Singular Value Decomposition Innovation Model Riccati Equation Covariance Sequence Model Reduction 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Faurre, In: System Identification: Advances and Case Studies (Eds. R.K. Mehra and D.G. Lainiotis), Academic Press, New York, 1976, pp. 1–25.CrossRefGoogle Scholar
  2. 2.
    R.J. Vaccaro and B.W. Dickinson, In:Proc. 19th Annual Asilomar Conf., Pacific Grove, CA, November, 1985.Google Scholar
  3. 3.
    M. Gevers and W.R.E Wouters, Journal A vol. 19, pp. 90–110, 1978.Google Scholar
  4. 4.
    B.D.O. Anderson and J.B. Moore, Optimal Filtering, Prentice-Hall, Englewood- Cliffs, 1979.MATHGoogle Scholar
  5. 5.
    H. Akaike, IEEE Trans. Automat. Contr. vol. AC-19, pp. 667–674, 1974.Google Scholar
  6. 6.
    B.L. Ho and R.E. Kaiman, In: Proc. 3rd Aller ton ConfMonticello, Illinois, pp.449- 459, 1965.Google Scholar
  7. J. Rissanen, SIAM J. Contr. vol. 9, pp. 420–430, 1971.MathSciNetCrossRefGoogle Scholar
  8. 8.
    R.E. Kaiman, In: Acta Polytechnica Scandinavica, Mathematics and Computer Science Series No. 31, pp. 9–32, 1979.Google Scholar
  9. 9.
    B.C. MooreIEEE Trans. Automat. Contr., vol. AC-26, pp. 17–32, 1981.CrossRefGoogle Scholar
  10. 10.
    L. Pernebo and L.M. Silverman, IEEE Trans. Automat. Contr. vol. AC-27, pp. 382–387, 1982.Google Scholar
  11. 11.
    R.J. Vaccaro, Ph.D. Dissertation, Princeton University, Princeton, NJ, 1983.Google Scholar
  12. 12.
    K.V. Fernando and H. Nicholson, IEEE Trans. Automat. Contr. vol. AC-28, pp. 228–231, 1983.MathSciNetCrossRefGoogle Scholar
  13. 13.
    V.C. Klema and A.J. LaubIEEE Trans. Automat. Contr. vol. AC-25, pp. 164–176, 1980.Google Scholar
  14. 14.
    K.S. Arun, D.V. Bhaskar Rao, and S.Y. Kung, In:Proc. 22nd IEEE Conf. Decision Contr. San Antonio, TX, pp. 1353–1355, 1983.Google Scholar
  15. 15.
    K.S. Arun and S.Y. Kung, In: Proc. IEEE Spectral Estimation Workshop II pp. 161–167, 1983.Google Scholar
  16. 16.
    S. Fujishige, S. Nagai, and Y. Sawaragi, Int. J. Contr. vol. 22, pp. 807–819, 1975.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    R.J. Vaccaro, IEEE Trans. Automat. Contr. vol. AC-30, pp. 921–923, 1985.MathSciNetCrossRefGoogle Scholar
  18. 18.
    A.J. Laub, In: Proc. 1980 JACC FA8-E, 1980.Google Scholar
  19. 19.
    U.B. Desai and D. Pal, In:Proc. 16th Annual Conf. Inform. Sei., Syst. Princeton Univ., Princeton, NJ, 1982; also in Proc. 22nd IEEE Conf. Decision, Contr. Orlando, FL, 1982.Google Scholar
  20. 20.
    U.B. Desai and D. Pal, IEEE Trans. Automat. Contr. vol. AC-29, pp. 1097–1100, 1984.MathSciNetCrossRefGoogle Scholar
  21. 21.
    J.A. Ramos and E.I. Verriest, In: Proc. American Contr. Conf. San Diego, CA, pp. 150–155, 1984.Google Scholar
  22. 22.
    C.I. Byrnes and A. Lindquist, Syst. Contr. Letters vol. 2, pp. 99–105, 1982. 23MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    R.J. Vaccaro, IEEE Proceedings (Letters) to appear, 1986.Google Scholar
  24. 24.
    Y. Baram, IEEE Trans. Automat. Contr. vol. AC-26, pp. 1225–1231, 1981.MathSciNetCrossRefGoogle Scholar
  25. 25.
    G.H. Golub, V.C. Klema, and G.W. Stewart, Stanford Univ. Tech. Rep. STAN-CS-76-559, Computer Sei. Dept., Stanford Univ., Palo Alto, CA, 1976.Google Scholar
  26. 26.
    H.P. Zeiger and A.J. McEwenIEEE Trans. Automat. Contr. p. 153, 1974.Google Scholar
  27. 27.
    S.Y. Kung, In: Proc. 12th Asilomar Conf. Pacific Grove, CA, pp. 705–714, 1978.Google Scholar

Copyright information

© Kluwer Academic Publishers, Boston 1986

Authors and Affiliations

  • Richard J. Vaccaro
    • 1
  1. 1.Department of Electrical EngineeringUniversity of Rhode IslandKingstonUSA

Personalised recommendations