A back propagation algorithm to estimate the parameters of non-linear dynamic rational models

Applied Mathematical Modelling

Volumn 27, Issue 3, 2003, Pages 169-187

  Zhu, Q M ^a  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

Author keywords

Back propagation computation; Model structure detection; Non linear rational models; Parameter estimation

Indexed keywords

ALGORITHMS; BACKPROPAGATION; MATHEMATICAL MODELS; PARAMETER ESTIMATION;

BACK PROPAGATION ALGORITHMS;

NONLINEAR SYSTEMS;

ALGORITHM;

EID: 0037367056     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(02)00097-5     Document Type: Article

References (27)

1. S.A. Billings, S. Chen, Identification of non-linear rational systems using a prediction error estimation algorithm, Int. J. Sys. Sci. 20 (1989) 467-494.
2. S.A. Billings, K.Z. Mao, Structure detection for nonlinear rational models using genetic algorithms, Int. J. Sys. Sci. 29 (1998) 223-231.
3. S.A. Billings, W.S.F. Woon, Structure detection and model validity tests in the identification of nonlinear systems, IEE Proc. Part D 130 (1983) 190-199.
4. S.A. Billings, Q.M. Zhu, Rational model identification using extended least squares algorithm, Int. J. Contr. 54 (1991) 529-546.
5. S.A. Billings, Q.M. Zhu, A structure detection algorithm for nonlinear dynamic rational models, Int. J. Contr. 59 (1994a) 1439-1463.
6. S.A. Billings, Q.M. Zhu, Nonlinear model validation using correlation tests, Int. J. Contr. 60 (1994b) 1107- 1120.
7. S.A. Billings, Q.M. Zhu, Model validation tests for multivariable nonlinear models including neural networks, Int. J. Contr. 62 (1995) 749-766.
8. S. Chen, S.A. Billings, Representations of nonlinear system: the NARMAX model, Int. J. Contr. 48 (1989)1013-1032.
9. S.D. Dimitrov, D.I. Kamenski, A parameter estimation method for rational functions, Comput. Chem. Eng. 15 (1991) 657-662.
10. I. Ford, D.M. Titterington, C.P. Kitsos, Recent advances in non-linear experimental design, Technometrics 31 (1989) 49-60.
11. R. Haber, H. Unbehauen, Structure identification of nonlinear dynamic system-a survey on input/output approaches, Automatica 26 (1990) 651-677.
12. S. Haykin, Neural Networks, Macmillan College Publishing Company, Oxford, 1994.
13. R.A. Jacobs, Increased rates of convergence through learning rate adaptation, Neural Networks 1 (1988) 295-307.
14. C. Kambhampati, J.D. Mason, K. Warwick, A stable one-step-ahead predictive control of nonlinear systems, Automatica 36 (2000) 485-495.
15. A.H. Kramer, A. Sangiovanni-Vincentelli, Efficient parallel learning algorithms for neural networks, in: D.S. Touretzky (Ed.), Advances in Neural Information Processing Systems, Morgan Kaufmann, San Mateo, CA, 1989, pp. 40-48.
16. H. Leung, S. Haykin, Rational function neural network, Neural Comput. 5 (1993) 928-938.
17. L. Ljung, Analysis of recursive stochastic algorithms, IEEE Trans. Autom. Contr. 22 (1977) 551-575.
18. K.S. Narendra, K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Networks 1 (1990) 4-27.
19. J.W. Ponton, The use of multivariable rational functions for non-linear data presentation and classiffication, Comput. Chem. Eng. 17 (1993) 1047-1052.
20. T. Proll, M.N. Karim, Model predictive PH control using real time NARX approach, AIChe J. 40 (1994) 269- 282.
21. D.E. Rumelhart, G.E. Hinton, R.J. Williams, Learning representations by back propagating errors, Nature (London) 323 (1986) 533-536.
22. E.D. Sontag, Realization theory of discrete time nonlinear systems: Part I-the bounded case, IEEE Trans. Circ. Syst. 26 (1978) 342-356.
23. E.D. Sontag, Polynomial Response Maps-Lecture Notes in Control and Information Sciences, vol. 13, Springer-Verlag, Berlin, 1979.
24. L.X Wang, Adaptive fuzzy systems and control, Prentice Hall, Englewood Cliffs, NJ, 1994.
25. Q.M. Zhu, S.A Billings, Recursive parameter estimation for nonlinear rational models, J. Sys. Eng. 1 (1991) 63-67.
26. Q.M. Zhu, S.A Billings, Parameter estimation for stochastic nonlinear models, Int. J. Contr. 57 (1993) 309-333.
27. Q.M. Zhu, Z. Ma, K. Warwick, Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete time systems, IEE Proc.-Contr. Theo. Appl. 146 (1999) 319-326.