Quasilinearization Method for System Identification

  • Robert Kalaba
  • Karl Spingarn
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG)


The method of quasilinearization was introduced in Chapter 4 as a successive approximation method for finding the solution of nonlinear two-point boundary problems. In this chapter quasilinearization is used for system identification (References 1–9) using the measurements to formulate the problem as a multipoint boundary-value problem. The least-squares criterion is used to estimate the unknown initial conditions and/or unknown parameters.


System Identification Unknown Parameter Nonlinear Dynamical System Quasilinearization Equation Successive Approximation Method 


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  1. 1.
    Bellman, R. E., and Kalaba, R. E., Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier Publishing Company, New York, 1965.MATHGoogle Scholar
  2. 2.
    Buell, J., and Kalaba, R. E., Quasilinearization and the fitting of nonlinear models of drug metabolism to experimental kinetic data, Mathematical Biosciences, Vol. 5, pp. 121–132, 1969.CrossRefGoogle Scholar
  3. 3.
    Kagiwada, H. H., System Identification, Methods and Applications, Addison-Wesley Publishing Company, Reading, Massachusetts, 1974.MATHGoogle Scholar
  4. 4.
    Eykhoff, P., System Identification, Parameter and State Estimation, John Wiley and Sons, Inc., New York, 1974.Google Scholar
  5. 5.
    Kalaba, R. E., and Spingarn, K., Optimal inputs and sensitivities for parameter estimation, Journal of Optimization Theory and Applications, Vol. 11, No. 1, pp. 56–67, 1973.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Bellman, R., Jacquez, J., Kalaba, R., and Schwimmer, S., Quasilinearization and the estimation of chemical rate constants from raw kinetic data, Mathematical Bio-sciences, Vol. 1, pp. 71–76, 1976.Google Scholar
  7. 7.
    Bellman, R., Kagiwada, H., and Kalaba, R., Orbit determination as a multi-point boundary-value problem and quasilinearization, Proceedings of the National Academy of Sciences, Vol. 48, No. 8, pp. 1327–1329, 1962.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Buell, J. D., Kagiwada, H. H., and Kalaba, R. E., A proposed computational method for estimation of orbital elements, drag coefficients, and potential fields parameters from satellite measurements, Annales de Geophysique, Vol. 23, No. 1, pp. 35–39, 1967.Google Scholar
  9. 9.
    Kumar, K. S. P., and Sridhar, R., On the identification of control systems by the quasilinearization method, IEEE Transactions on Automatic Control, Vol. 9, No. 2, pp. 151–154, 1964.MathSciNetCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • Robert Kalaba
    • 1
  • Karl Spingarn
    • 2
  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.Hughes Aircraft CompanyLos AngelesUSA

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