Non-parametric identification of dynamic non-linear systems by a Hermite series approach

International Journal of Systems Science

Volumn 32, Issue 10, 2001, Pages 1261-1285

  Krzyzak, Adam ^a   Sa̧siadek, Jerzy Z ^a   Kégl, Balázs ^a  

^a Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONTROL NONLINEARITIES; CONVERGENCE OF NUMERICAL METHODS; IDENTIFICATION (CONTROL SYSTEMS); SYSTEM STABILITY;

HAMMERSTEIN SYSTEM; HERMITE SERIES APPROACH; WIENER SYSTEM;

NONLINEAR CONTROL SYSTEMS;

EID: 0035496950     PISSN: 00207721     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207720110045056     Document Type: Article

References (46)

1. Bendat, J., 1990, Nonlinear System Analysis and Identification from Random Data (New York: Wiley).
2. Bosq, D., and Bleuez, J., 1978. Etude d'une classe d'estimateurs non-parametriques de la densite. Annals de l'Institut Henri Poincare, 14, 479-498.
3. Box, G., and Jenkins, G., 1976, Time Series Analysis Forecasting and Control (San Francisco: Holden Day).
4. Chang, F. H., and Luus, R., 1971, A noniterative method for identification using Hammerstein system. IEEE Transactions on Automatic Control, AC-16, 464-468.
5. Chung, H., and Sun, Y. Y., 1988, Analysis and parameter estimation of nonlinear systems with Hammerstein model using Taylor series approach. IEEE Transactions on Circuits Systems, CAS-35, 1533-1544.
6. Devroye, L., and Györfi, L., 1985, Nonparametric Density Estimation. The L1 View. (New York: Wiley).
7. Devroye, L., Györfi, L., and Lugosi, G., 1996, A Probabilistic Theory of Pattern Recognition (New York: Springer).
8. Efron, B., and Tibshirani, R., 1993, An Introduction to the Boostrap (New York: Chapman & Hall).
9. Emerson, R., Korenberg, M., and Citron, M., 1992, Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex. Biological Cybernetics, 66, 291-300.
10. Eubank, R., 1999, Spline Smoothing and Nonparametric Regression (New York: Marcel Dekker).
11. Gallman, P., 1976. A comparison of two Hammerstein model identification algorithms. IEEE Transactions on Automatic Control, AC-21, 124-126.
12. Greblicki, W., 1989, Non-parametric orthogonal series identification of Hammerstein systems. International Journal of Systems Science, 326, 2355-2367.
13. Greblicki, W., and Krzyzak, A., 1979, Non-parametric identification of a memoryless system with cascade structure. International Journal of Systems Science, 10, 1301-1310.
14. Greblicki, W., and Pawlak, M., 1985, Fourier and Hermite series estimates of regression functions. Annals of the Institute of Statistical Mathematics, 37, Part A, 443-454.
15. Greblicki, W., and Pawlak, M., 1987, Hammerstein system identification by nonparametric regression estimation. International Journal of Control., 45, 343-354.
16. Greblicki, W., and Pawlak, M., 1989, Recursive nonparametric identification of Hammerstein systems. Journal of the Franklin Institute, 326, 461-481.
17. Györfi, L., Härdle, W., Sarda, P., and Vieu, P., 1989, Nonparametric Curve Estimation from Time Series. (Berlin: Springer).
18. Haber, R., and Unbehauen, H., 1990, Structure identification of nonlinear dynamic systems - a survey on input/output approaches. Automatica, 26, 651-677.
19. Hall, P., 1989, On convergence rates in nonparametric problems. International Statistics Review, 57, 45-58.
20. Hsia, T., 1977, System Identification (Lexington: D.C. Heath & Company).
21. Hunter, I., and Korenberg, M., 1986, The identification of non-linear biological systems: Wiener and Hammerstein cascade models. Biological Cybernetics, 55, 135-144.
22. Korenberg, M. J., and Hunter, I., 1986, The identification of non-linear biological systems: LNL cascade models. Biological Cybernetics, 55, 125-134.
23. Krzyzak, A., 1989, Identification of discrete Hammerstein systems by the Fourier series regression estimate. International Journal of Systems Science, 20, 1729-1744.
24. Krzyzak, A., 1990, On estimation of a class of nonlinear systems by the kernel regression estimate. IEEE Transactions on Information Theory, IT-36, 141-152.
25. Krzyzak, A., 1992, Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation. IEEE Transactions on Information Theory, IT-38, 1323-1338.
26. Krzyzak, A., 1996, On nonparametric estimation of nonlinear dynamic systems by the Fourier series estimate. Signal Processing, 52, 299-321.
27. Krzyzak, A., and Partyka, M., 1993, Identification of block oriented systems by nonparametric techniques. International Journal of Systems Science, 24, 1049-1066.
28. Kung, M., and Womàck, B., 1984, Discrete-time adaptive control of linear dynamic systems with a two-segment piecewise-linear asymmetric nonlinearity. IEEE Transactions on Automatic Control, AC-29, 170-172.
29. Leontaritis, I., and Billings, S., 1985, Input-output parametric models for non-linear systems. Part II: stochastic non-linear systems. International Journal of Control, 41, 329-344.
30. Marmarelis, P., and Marmarelis, V., 1978, Analysis of Physiological Systems: The White Noise Approach (New York: Plenum).
31. Masry, E., and Cambanis, S., 1980, Signal identification after noisy, nonlinear transformations. IEEE Transactions on Information Theory, IT-26, 50-58.
32. Masry, T., and Cambanis, S., 1981 Consistent estimation of continuous-time signals from nonlinear transformations of noisy samples. IEEE Transactions on Information Theory, IT-27, 84-96.
33. McCannon, T., Gallagher, W., Minoo-Hamedani, D., and Wise, G., 1982, On the design of nonlinear discrete-time predictors. IEEE Transactions on Information Theory, IT-28, 366-371.
34. Müller, H., 1988, Nonparametric Regression Analysis of Longitudinal Data (Berlin: Springer).
35. Narendra, K., and Gallman, P., 1966, An iterative method for the identification of nonlinear systems using the Hammerstein model. IEEE Transactions on Automatic Control, AC-11, 546-550.
36. Papoulis, A., 1990, Probability and Statistics (Englewood Cliffs: Prentice Hall).
37. Sandberg, I., 1991, Approximation theorems for discrete-time systems. IEEE Transactions on Circuits and Systems, CAS-38, 564-566.
38. Sandberg, I., 1992, Approximations of nonlinear functionals. IEEE Transactions on Circuits and Systems, CAS-39, 65-67.
39. Sansone, G., 1959, Orthogonal Functions (Wiley-Interscience: New York).
40. Sawchuck, A., and Strand, T., 1982, Fourier optics in nonlinear image processing. In: H. Stark (ed.) Applications of Optical Fourier Transforms (New York: Academic Press), pp. 391-429.
41. Schetzen, M., 1980, The Volterra and Wiener Theories of Nonlinear Systems (New York: Wiley-Interscience).
42. Schartz, S., 1967, Estimation of probability density by an orthogonal series. Annals of Mathematics and Statistics, 38, 1261-1265.
43. Stapleton, J., and Baas, S., 1985, Adaptive noise cancelation for a class of nonlinear, dynamic reference channels. IEEE Transactions on Circuits and Systems, CAS-32.
44. Szegö, G., 1967, Orthogonal Polynomials (Providence: American Mathematical Society).
45. Walter, G., 1977, Properties of Hermite series estimation of probability density. Annals of Statistics, 5, 1258-1264.
46. Wiener, N., 1958, Nonlinear Problems in Random Theory (Wiley: New York).