On the Series Expansion Approach to the Identification of Hammerstein Systems

IEEE Transactions on Automatic Control

Volumn 36, Issue 6, 1991, Pages 763-767

  Pawlak, Miroslaw ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--POLYNOMIALS;

CONVERGENCE RATES; GLOBAL CONSISTENCY; HAMMERSTEIN SYSTEMS IDENTIFICATION; LEGENDRE ORTHOGONAL SYSTEM; POLYNOMIAL IDENTIFICATION ALGORITHM; SERIES EXPANSION APPROACH;

CONTROL SYSTEMS;

EID: 0026171066     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.86954     Document Type: Article

References (24)

1. H. Akaike, “A new look at statistical model identification,” IEEE Trans. Automat. Contr., vol. AC-13, pp. 716–723, 1974.
2. S. A. Billings and S. Y. Fakhouri, “Identification of a class of nonlinear systems using correlation analysis,” Proc. IEE, vol. 125, pt. D., pp. 631–697, 1978.
3. D. R. Brillinger, “The identification of a particular nonlinear time series system,” Biometrika, vol. 64, pp. 509–515, 1977.
4. H. Y. Chung and Y. Y. Sun, “Analysis and parameter estimation of nonlinear systems with Hammerstein model using Taylor series approach,” IEEE Trans. Circuits Syst., vol. CAS-35, pp. 1533–1544, 1988.
5. P. Diggle and P. Hall, “The selection of terms in an orthogonal series density estimator,” J. Amer. Statist. Assoc., vol. 81, pp. 230–233, 1986.
6. R. L. Eubank, Spline Smoothing and Nonparametric Regression. New York: Marcel-Dekker, 1988.
7. W. Greblicki and M. Pawlak, “Identification of discrete Hammerstein systems using kernel regression estimates,” IEEE Trans. Automat. Contr., vol. AC-31, pp. 74–77, 1986.
8. “Hammerstein system identification by nonparametric regression estimation,” Int. J. Contr., vol. 45, pp. 343–354, 1987.
9. “Recursive nonparametric identification of Hammerstein systems,” J. Franklin Inst., vol. 326, pp. 461–481, 1989.
10. “Nonparametric identification of Hammerstein systems,” IEEE Trans. Inform. Theory, vol. IT-35, pp. 409–418, 1989.
11. “Hermite series estimates of a probability density and its derivatives,” J. Multivariate Anal., vol. 15, pp. 176–182, 1984.
12. “Fourier and Hermite series estimates of regression functions,” Ann. Inst. Statist. Math., vol. 37, pp. 443–459, 1985.
13. P. Hall, “Comparison of the orthogonal series methods of estimating a density and its derivatives on an interval,” J. Multivariate Anal., vol. 12, pp. 432–449, 1982.
14. W. Hardle, P. Hall, and S. Marron, “How far are automatically chosen regression smoothing parameters from their optimum,” J. Amer. Statist. Assoc., vol. 83, pp. 86–110, 1988.
15. J. D. Hart, “On the choice of a truncation point in Fourier series density estimator,” J. Statist. Computation Simulation, vol. 21, pp. 95–116, 1985.
16. I. W. Hunter and M. J. Korenberg, “The identification of nonlinear biological systems: Wiener and Hammerstein cascade models,” Biol. Cybern., vol. 55, pp. 135–144, 1986.
17. C. Hwang and K. K. Shyu, “Series expansion approach to the analysis and identification of discrete Hammerstein systems,” Int. J. Contr., vol. 47, pp. 1961–1972, 1988.
18. K. S. Narendra and P. G. Gallman, “An iterative method for the identification of nonlinear systems using the Hammerstein model,” IEEE Trans. Automat. Contr., vol. AC-11, pp. 546–550, 1966.
19. P. N. Paraskevopoulos, “Legendre series approach to the identification and analysis of linear systems,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 585–588, 1985.
20. G. Sansone, Orthogonal Functions. New York: Interscience, 1959.
21. D. H. Shih and F. C. Kung, “Optimal control of deterministic systems via shifted Legendre polynomials,” IEEE Trans. Automat. Contr., vol. AC-31, pp. 951–954, May 1986.
22. “The shifted Legendre approach to nonlinear system analysis and identification,” Int. J. Contr., vol. 42, pp. 1399–1410, 1985.
23. P. Stoica, “On the convergence of an iterative algorithm used for Hammerstein system identification,” IEEE Trans. Automat. Contr., vol. AC-26, pp. 967–969, 1981.
24. G. Szego, Orthogonal Polynomials. New York: Amer. Math. Soc., 1959.