Identification of non-linear stochastic systems by state dependent parameter estimation

International Journal of Control

Volumn 74, Issue 18, 2001, Pages 1837-1857

  Young, Peter C ^a   Mckenna, Paul ^a   Bruun, John ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DYNAMIC PROGRAMMING; ERROR ANALYSIS; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION; PARAMETER ESTIMATION; SIGNAL PROCESSING; STATE ESTIMATION; STOCHASTIC CONTROL SYSTEMS; TIME VARYING CONTROL SYSTEMS;

NON-LINEAR STOCHASTIC SYSTEMS;

NONLINEAR CONTROL SYSTEMS;

EID: 0035895094     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207170110089824     Document Type: Article

References (52)

1. Brown, R.L., Durbin, J., and Evans, J.M., 1975, Techniques for testing the constancy of regression relationships over time, Journal Royal Statistical Society, Series B, 37, 141-192.
2. Bryson, A.E., and Ho, Y.C., 1969, Applied Optimal Control (Blaisdel).
3. Co, T., 1996, Parameter estimation of non-linear systems using modulating functions methods. In M. I. Friswell and J. E. Mottershead (Eds), Identification in Engineering Systems, University of Wales, Swansea, UK, pp. 87-96.
4. Daubechies, I., 1988, Orthonormal bases of compactly supported wavelets, Communications on Pure Applied Mathematics, 41, 906-966.
5. Dempster, A.P., Laird, N.M., and Rubin, D.B., 1977, Maximum likelihood from incomplete data via the EM algorithm, Journal Royal Statistical Society, Series B, 39, 1-38.
6. Durbin, J., and Koopmans, S.J., 1999, Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives. Journal of the Royal Statistical Society, Series B, 62, (in press).
7. Gamerman, D., 1997, Markov Chain Monte Carlo (Chapman and Hall).
8. Gauss, K.F., 1821, 1823, 1826, Theoria combinationis observationum erroribus minimis obnoxiae, Parts 1, 2 and supplement, Werke, 4, 1-108.
9. Harvey, A.C., 1981, Time Series Models (Oxford: Phillip Allen, Oxford).
10. Harvey, A.C., 1984, A unified view of statistical forecasting procedures (with comments). Journal of Forecasting, 3, 245-283.
11. Harvey, A.C., 1989, Forecasting Structural Time Series Models and the Kalman Filter (Cambridge University Press).
12. Harvey, A.C., and PETERS, S., 1990, Estimation procedures for structural time series models, Journal of Forecasting, 9, 173-204.
13. Hastie, T.J., and Tibshirani, R.J., 1996, Generalized Additive Models (Chapman and Hall).
14. Hoberock, L.L., and Kohr, R.H., 1966, An experimental determination of differential equations to describe simple non-linear systems. Preprints, Joint Automatic Control Conference, Seattle, Washington, USA.
15. Holst, U., Hössjer, O., Björklund, C., Ragnarsson, P., and Edner, H., 1996, Locally weighted least squares kernel regression and statistical evaluation of LIDAR measurements, Environmetrics, 7, 410-416.
16. Hu, J., Kumamaru, K., and Hirasawa, K., 2001, A quasi-ARMAX approach to modelling non-linear systems. International Journal of Control, this special issue.
17. Jakeman, A.J., and Young, P.C., 1979, Recursive filtering and the inversion of ill-posed causal problems, CRES Report No. AS/R28/1979, Centre for Resource and Environmental Studies, Australian National University.
18. Jakeman, A.J., and Young, P.C., 1984, Recursive filtering and the inversion of ill-posed causal problems. Utilitas Mathematica, 35, 351-376.
19. Kalman, R.E., 1960, A new approach to linear filtering and prediction problems. ASME Transactions Journal Basic Engineering, 82D, 35-45.
20. Kitagawa, G., 1981, A non-stationary time series model and its fitting by a recursive filter. Journal of Time Series Analysis, 2, 103-116.
21. Lee, R.C.K., 1964, Optimal Identification, Estimation and Control. (MIT Press).
22. McCabe, A., Chotai, A., and Young, P.C., 2001, State dependent parameter PIP control of non-linear systems. Report No. TR/175, Centre for Research on Environmental Systems and Statistics, Lancaster University.
23. Mees, A.I., 1991, Dynamical systems and tesselations: detecting determinism in data. International Journal of Bifurcation and Chaos, 1, 777-794.
24. Mees, A.I., 1993, Parsimonious dynamical reconstruction, International Journal of Bifurcation and Chaos, 3, 669-675.
25. Mees, A.I., Aihara, K., Adachi, M., Judd, K., Ikeguchi, T., and Massumoto, G., 1992, Deterministic prediction and chaos in squid axon response. Physics Letters A, 169, 41-45.
26. Mendel, J.M., 1969, A priori and a posteriori identification of time varying parameters. Second Hawaii International Conference on System Sciences.
27. Norton, J.P., 1976, Identification by optimal smoothing using integrated random walks. Proceedings of the Institute Electrical Engineers, 123, 451-452.
28. Norton, J.P., 1986, An Introduction to Identification (Academic Press).
29. Plackett, R.L., 1950, Some theorems in least squares. Biometrika, 37, 149-157.
30. Priestley, M.B., 1988, Nonlinear and Nonstationary Time Series Analysis (Academic Press).
31. Ruanaidh, J.J., and Fitzgerald, W.J., 1996, Numerical Bayesian Methods Applied to Signal Processing (Springer).
32. Schweppe, F., 1965, Evaluation of likelihood function for Gaussian signals. IEEE Transactions on Information Theory, 11, 61-70.
33. Taylor, C.J., Young, P.C., and Chotai, A., 2000, State space control system design based on non-minimal state variable feedback: further generalisations and unification results, International Journal of Control, 73, 1329-1345.
34. Young, P.C., 1969, Applying parameter estimation to dynamic systems: Part 1, Theory. Control Engineering, 16, 119-125; Part II Applications, 16, 118-124.
35. Young, P.C., 1969, Applying parameter estimation to dynamic systems: Part 1, Theory. Control Engineering, 16, 119-125; Part II Applications, 16, 118-124.
36. Young, P.C., 1970, An instrumental variable method for realtime identification of a noisy process. Automatica, 6, 271-287.
37. Young, P.C., 1978, A general theory of modeling for badly defined dynamic systems. In G. C. Vansteenkiste (Ed.), Modeling, Identification and Control in Environmental Systems (North Holland), 103-135.
38. Young, P.C., 1984, Recursive Estimation and Time-Series Analysis (Springer).
39. Young, P.C., 1988, Recursive extrapolation, interpolation and smoothing of non-stationary time-series. In H. F. Chen (Ed.) Identification and System Parameter Estimation 1988 (Pergamon Press), pp. 33-44.
40. Young, P.C., 1989, Recursive estimation and modelling of non-stationary and non-linear time-series. In IFAC Symposium on Adaptive Systems in Control and Signal Processing, Vol. 1 (Pergamon Press), pp. 49-64.
41. Young, P.C., 1993, Time variable and state dependent modelling of non-stationary and non-linear time series In T. Subba RaG (Ed.), Developments in Time Series Analysis (Chapman and Hall), pp. 374-413.
42. Young, P.C., 1994, Time-variable parameter and trend estimation in non-stationary economic time series. Journal of Forecasting, 13, 179-210.
43. Young, P.C., 1996, A general approach to identification, estimation and control for a class of non-linear dynamic systems. In M. I. Friswell and J. E. Mottershead (Eds), Identification in Engineering Systems (Swansea: University of Wales), pp. 436-445.
44. Young, P.C., 1998, Data-based mechanistic modelling of environmental, ecological, economic and engineering systems. Environmental Modelling and Software, 13, 105-122.
45. Young, P.C., 1999, Nonstationary time series analysis and forecasting. Progress in Environmental Science, 1, 3-48.
46. Young, P.,C., 2000, Stochastic, dynamic modelling and signal processing: time variable and state dependent parameter estimation. In W. J. Fitzgerald, A. Walden, R. Smith and P. C. Young (Eds) Nonlinear and Nonstationary Signal Processing (Cambridge: Cambridge University Press), pp. 74-114.
47. Young, P.C., 2001 a, The identification and estimation of non-linear stochastic systems. In A. I. Mees (Ed.) Nonlinear Dynamics and Statistics (Boston: Birkhauser), pp. 127-166.
48. Young, P.C., 2001 b, Comment on 'A quasi-ARMAX approach to the modelling of non-linear systems' by J. Hu et al., International Journal of Control, this special issue.
49. Young, P.C., and Beven, K.J., 1994, Data-based mechanistic modelling and the rainfall-flow non-linearity. Environmetrics, 5, 335-363.
50. Young, P.C., and Pedregal, D.J., 1998, Recursive and enbloc approaches to signal extraction. Journal of Applied Statistics, 26, 103-128.
51. Young, P.C., Pedregal, D.J., and Tych, W., 1999, Dynamic harmonic regression. Journal of Forecasting, 18, 369-394.
52. Zhan-Qian, J.L., and Smith, R.L., 1998, Estimating local Lyapunov exponents by local polynomial regression, University of North Carolina, Department of Statistics, http://www.stat.unc.edu./postcript/rs/chaos.