On the approximation of time-varying stochastic systems

  • R. Genesio
  • R. Pomé
Optimal Control Stochastic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


A linear time-varying stochastic system described in terms of input-output data corrupted by noise is given and an optimal, time-invariant, low-order approximating model is required. After the problem statement, the paper introduces an input-independent criterion and then considers the problem of its evaluation from the available data. A procedure is developed in order to obtain in closed form the upper bound, corresponding to a given level of probability, of the error functional. Finally, the minimization of this quantity leads to the optimal model parameters and to the approximation measure.


Optimal Model Parameter Positive Definite Weighting Additive Random Noise Model Impulse Response Linear Weighting Function 
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.


  1. [1]
    R. Genesio and M. Milanese: "A note on derivation and use of reduced order models" — IEEE Trans. Automat. Contr., vol. AC-21, Feb. 1976.Google Scholar
  2. [2]
    C.F. Chen and L.S. Shieh: "A novel approach to linear model simplification" — Int. J. Contr., vol. 8, pp. 561–570, 1968.Google Scholar
  3. [3]
    M.R. Chidambara: "Two simple techniques for the simplification of large dynamic systems" — Proc. JACC '69, pp. 669–674, 1969.Google Scholar
  4. [4]
    T.C. Hsia: "On the simplification of linear systems" — IEEE Trans. Autom. Contr., vol; AC-17, pp. 372–374, 1972.Google Scholar
  5. [5]
    H. Heffes and P.E. Sarachik: "Uniform approximation of linear systems" — Bell Syst. Tech. J., vol. 48, pp. 209–231, 1969.Google Scholar
  6. [6]
    M. Milanese and A. Negro: "Uniform approximation of systems. A Banach space approach" — J.O.T.A., vol. 12, pp. 203–217, 1973.Google Scholar
  7. [7]
    R.J.P. De Figuereido, A. Caprihan and A.N. Netrevali: "On optimal modeling of systems" — J.O.T.A., vol. 11, pp. 68–83, 1973.Google Scholar
  8. [8]
    G.J. Bierman: "Weighted least squares stationary approximations to linear systems" — IEEE Trans. Automat. Contr., vol. AC-17, pp. 232–234, 1972.Google Scholar
  9. [9]
    H. Nosrati and H.E. Meadows: "Modeling of linear time-varying systems by linear time-invariant systems of lower order" — IEEE Trans. Automat. Contr., vol. AC-18, pp. 50–52, 1973.Google Scholar
  10. [10]
    W.L. Root: "On the measurement and use of time-varying communication channelss` — Inform. and Contr., vol. 8, pp. 390–422, 1965.Google Scholar
  11. [11]
    I. Bar-David: "Estimation of linear weighting functions in Gaussian noise" — IEEE Trans. Inform. Theory, vol. IT-14, pp. 288–293, 1968.Google Scholar
  12. [12]
    P.A. Bello: "Measurement of random time-variant linear channels" — IEEE Trans. Inform. Theory, vol. IT-15, pp. 469–475, 1969.Google Scholar
  13. [13]
    E. Mosca: "A deterministic approach to a class of nonparametric system identification problems" — IEEE Trans. Inform. Theory, vol. IT-17, pp. 686–696, 1971.Google Scholar
  14. [14]
    N.I. Akhiezer and I.M. Glazman: "Theory of Linear Operators in Hilbert Space", vol. I, F. Ungar, New York, 1966.Google Scholar
  15. [15]
    R. Deutsch: "Estimation Theory", Prentice-Hall, Englewood Cliffs, 1965.Google Scholar
  16. [16]
    F.R. Gantmacher: "The Theory of Matrices", vol. I, Chelsea, New York, 1959.Google Scholar
  17. [17]
    R. Genesio and R. Pomé: "Identification of reduced models from noisy data" — Int. J. Contr., vol. 21, pp. 203–211, 1975.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • R. Genesio
    • 1
  • R. Pomé
    • 1
  1. 1.CENS - Politecnico di TorinoIstituto Elettrotecnico Nazionale Galileo FerrarisTorinoItaly

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