Direct approach to identification of nonlinear differential models from discrete data

Mechanical Systems and Signal Processing

Volumn 13, Issue 5, 1999, Pages 739-755

  Coca, D ^a   Billings, S A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA STRUCTURES; KALMAN FILTERING; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARAMETER ESTIMATION; SPURIOUS SIGNAL NOISE;

DISCRETE DATA; NONLINEAR DIFFERENTIAL MODELS;

DIFFERENTIAL EQUATIONS;

EID: 0033340605     PISSN: 08883270     EISSN: None     Source Type: Journal    
DOI: 10.1006/mssp.1999.1230     Document Type: Article

References (28)

1. UNBEHAUEN H., RAO G. P. Identification of Continuous Systems. 1987;North-Holland, Amsterdam.
2. SINHA N. K., RAO G. P. Identification of Continuous-Time Systems. 1991;Kulwer Academic, Dordrecht.
3. YOUNG P. C. Parameter estimation for continuous-time models - a survey. Automatica. 17:1981;23-39.
4. PATRA A., UNBEHAUEN H. Identification of a class of nonlinear continuous-time systems using Hartley modulating functions. International Journal of Control. 62:1995;1431-1451.
5. TSANG K. M., BILLINGS S. A. Reconstruction of linear and nonlinear continuous-time models from discrete-time sampled data systems. Mechanical Systems and Signal Processing. 6:1992;69-84.
6. FIORETTI S., JETTO L. Accurate derivative estimation from noisy data: A state-space approach. International Journal of Systems Science. 20:1989;33-53.
7. COCA D., BILLINGS S. A. Continuous-time system identification for linear and nonlinear systems using wavelet decompositions. International Journal of Bifurcation and Chaos. 7:1997;87-96.
8. YOUNG P. C. Time variable and state dependent parameter modelling of nonstationary and nonlinear time series. Rao T. S. Developments in Time Series Analysis. 1993;374-413 Chapman & Hall, London.
9. YOUNG P. C. Data based mechanistic modelling of engineering systems. Journal of Vibration and Control. 4:1998;5-28.
10. YOUNG P. C., FOSTER M., LEES M. A direct approach to the identification and estimation of continuous-time systems from discrete-time data based on fixed interval smoothing. Proceedings of the12th Triennial World Congress of the International Federation of Automatic Control. 1993;Pergamon, Oxford. p. 647-650.
11. CHEN S., BILLINGS S. A. Representations of non-linear systems: the NARMAX model. International Journal of Control. 49:1989;1013-1032.
12. CHEN S., BILLINGS S. A., LUO W. Orthogonal least-squares methods and their applications to nonlinear system identification. International Journal of Control. 50:1989;1873-1896.
13. YOUNG P. C. Recursive Estimation and Time Series Analysis. 1984;Springer-Verlag, Berlin.
14. ANDERSON B. D. O., MOORE J. B. Optimal Filtering. 1979;Prentice-Hall, Englewood Cliffs.
15. JAKEMAN A. J., YOUNG P. C. Joint parameter-state estimation. Electronics Letters. 15:1979;582.
16. JAKEMAN A. J., YOUNG P. C. Recursive filtering and the inversion of ill posed causal problems. Utilitas Mathematica. 35:1984;351-376.
17. YOUNG P. C., NG C. N. Variance intervention. Journal of Forecasting. 8:1989;399-416.
18. NG C. N., YOUNG P. C. Recursive estimation and forecasting of non-stationary time series. Journal of Forecasting. 9:1990;173-204.
19. YOUNG P. C. Recursive extrapolation, interpolation and smoothing of non-stationary time series. Chen C. F. Identification and System Parameter Estimation. 1988;33-44 Pergamon Oxford.
20. LEWIS F. L. Optimal Estimation. 1986;Wiley, New York.
21. NIEDŹWIECKI M., SETHARES A. Smoothing of discontinuous signals: the competitive approach. IEEE Transactions on Signal Processing. 43:1995;1-13.
22. BILLINGS S. A., CHEN S. Extended model set, global data and threshold model identification of severely nonlinear systems. International Journal of Control. 50:1989;1897-1923.
23. CHUA L. O. The genesis of Chua's circuit. Archiv für Elektronik und Übertragungstechnik. 46:1992;250-257.
24. MATSUMOTO T., KOMURO M., KOKUBU H., TOKUNAGA R. Bifurcations. Sights Sounds and Mathematics. 1993;Springer-Verlag, Tokyo.
25. KENNEDY M. P. Three steps to chaos - Part II: A Chua's circuit primer. IEEE Transactions on Circuits and Systems-1: Fundamental Theory and Applications. 40:1993;657-674.
26. DEDIEU H., OGORZALEK M. Controlling chaos in Chua's circuit via sampled inputs. International Journal of Bifurcation and Chaos. 4:1994;447-455.
27. COCA D., BILLINGS S. A. Direct parameter identification of distributed parameter systems. Int. J of Systems Science. 1998.
28. MEDITCH J. S. A survey of data smoothing for linear and nonlinear dynamic systems. Automatica. 9:1973;151-162.