Neural networks for nonlinear dynamic system modelling and identification

REFERENCES

• BEALE , R. , and JACKSON , T. , 1990 , Neural Computing an Introduction ( Bristol , U.K. Adam Hilger ).
   Google Scholar
• BILLINGS , S. A. , 1980 , Identification of nonlinear systems-a survey . Proceedings of the Institution of Electrical Engineers , Pt D , 127 , 272 – 285 .
   Google Scholar
• BILLINGS , S. A. , and CHEN , S. , 1989 a, Identification of non-linear rational systems using a prediction-error estimation algorithm. International Journal of Systems Science , n20 n, 467 – 494 1989 b, Extended model set, global data and threshold model identification of severely non-linear systems. International Journal of Control, 50, 1897-1923 .
   Web of Science ®Google Scholar
• BILLINGS , S. A. , CHEN , S. , and KORENBERG , M. J. , 1989 , Identification of MIMO non-linear systems using a forward-regression orthogonal estimator . International Journal of Control , n49 n, 2157 – 2189 .
   Web of Science ®Google Scholar
• BILLINGS , S. A. , GRAY , J. O. , and OWENS , D. H. , (editors), 1984 , Nonlinear System Design ( London Peter Peregrinus ).
   Google Scholar
• BILLINGS , S. A. ,LEONTARITIS, I, J., 1981 , Identification of nonlinear systems using parameter estimation techniques . Proceedings of the IEE Conference on Control and Its Applications , Warwick, U.K., pp. 183 – 187 .
   Google Scholar
• BJÖRCK , A. , 1967 , Solving linear least squares problems by Gram-Schmidt orthogonalization , Nor disk Tidskr. Informations-Behandling , 7 , 1 – 21 .
   Google Scholar
• BROOMHEAD , D. S. , and LOWE , D. , 1988 , Multivariable functional interpolation and adaptive networks . Complex Systems, 2 , 321 – 355 .
   Google Scholar
• CHEN , S. , and BILLINGS , S. A. , 1989 a , Recursive prediction error estimator for nonlinear models . International Journal of Control , 49 , 569 – 594 ; 1989 b, Representation ofnonlinear systems the NARMAX model. Ibid., 49, 1013–1032; 1989c, Modelling and analysis of nonlinear time series. Ibid., 50, 2151–2171 .
   Web of Science ®Google Scholar
• CHEN , S. , BILLINGS , S. A. , COWAN , C. F. N. , and GRANT , P. M. , 1990 c, Practical identification of NARMAX models using radial basis functions . International Journal of Control , n52 n, 1327 – 1350 .
   Web of Science ®Google Scholar
• CHEN , S. , BILLINGS , S. A. , and GRANT , P. M. , 1990 a , Non-linear systems identification using neural networks . International Journal of Control , 51 , 1191 – 1214 ; 1992, Recursive hybrid algorithm for non-linear system identification using radial basis function networks. Ibid., 55, 1051–1070 .
   Web of Science ®Google Scholar
• CHEN , S. , BILLINGS , S. A. , and Luo , W. , 1989 , Orthogonal least squares methods and their application to nonlinear system identification . International Journal of Control , n50 n, 1873 – 1896 .
   Web of Science ®Google Scholar
• CHEN , S. , COWAN, C. F, N., BILLINGS , S. A. , and GRANT , P. M. , 1990 b, Parallel recursive prediction error algorithm for training layered neural networks . International Journal of Control , n51 n, 1215 – 1228 .
   Web of Science ®Google Scholar
• CHEN , S. , COWAN, C, F. N., and GRANT , P. M. , 1991 a, Orthogonal least squares learning algorithm for radial basis function networks . IEEE Transactions on Neural Networks , n2 n, 302 – 309 .
   Web of Science ®Google Scholar
• CHEN , S. , GRANT , P. M. , and COWAN , C. F. N. , 1991 b , Orthogonal least squares algorithm for training multi-output radial basis function networks . Proceedings of the 2nd I.E.E. International Conference on Artificial Neural Networks , Bournemouth , U. K. ,
   Google Scholar
• CYBENKO , G. , 1989 , Approximations by superpositions of a sigmoidal function . Mathematics of Control, Signals and Systems , n2 n, 303 – 314 .
   Google Scholar
• DUDA , R. O. , and HART , P. E. , 1973 , Pattern Classification and Scene Analysis ( New York Wiley ).
   Google Scholar
• FUNAHASHI , K. , 1989 , On the approximate realization of continuous mappings by neural networks . Neural Networks , n2 n, 183 – 192 .
   Web of Science ®Google Scholar
• GOLUB , G. , 1965 , Numerical methods for solving linear least squares problems . Numerische Mathematik , 7 , 206 – 216 .
   Google Scholar
• GOODWIN , G. C. , and PAYNE , R. L. , 1977 , Dynamic System Identification Experiment Design and Data Analysis ( New York Academic Press ).
   Google Scholar
• HECHT-NIELSEN , R. , 1990 , Neurocomputing ( Reading , Mass Addison-Wesley ).
   Google Scholar
• HORNIK , K. , 1991 , Approximation capabilities of multilayer feedforward networks . Neural Networks , n4 n, 251 – 257 .
   Web of Science ®Google Scholar
• KOHONEN , T. , 1987 , Self-Organization and Associative Memory ( Berlin Springer-Verlag ).
   Google Scholar
• LAPEDES , A. , and FARBER , R. , 1988 , How neural nets work. Neural Information Processing Systems , edited by D. Z. Anderson ( New York American Institute of Physics ), pp. 442 – 456 .
   Google Scholar
• LEONTARITIS , I. J. , and BILLINGS , S. A. , 1985 , Input-output parametric models for non-linear systems-Part 1 Deterministic non-linear systems; Part 2 Stochastic non-linear systems . International Journal of Control , 41 , 303 – 344 ; 1987, Model selection and validation methods for non-linear systems. International Journal of Control, 45, 311–341 .
   Web of Science ®Google Scholar
• LIPPMANN , R. P. , 1987 , An introduction to computing with neural nets . IEEE Acoustics, Speech and Signal Processing Magazine , n4 n.
   Google Scholar
• LIUNG , L. , and SODERSTROM , T. , 1983 , Theory and Practice of Recursive Identification ( Cambridge , Mass MIT Press ).
   Google Scholar
• MEAD , C. , 1989 , Analog VLSI and Neural Systems ( Reading , Mass Addison-Wesley ).
   Google Scholar
• MOODY , J. , and DARKEN , C. , 1989 , Fast-learning in networks of locally-tuned processing units . Neural Computation , n1 n, 281 – 294 .
   Web of Science ®Google Scholar
• NARENDRA , K. S. , and PARTHASARATHY , K. , 1990 , Identification and control of dynamical systems using neural networks . IEEE Transactions on Neural Networks , n1 n, 4 – 27 .
   Google Scholar
• OZAKI , T. , 1985 , Non-linear time series models and dynamical systems . Handbook of Statistics 5 Time Series in the Time Domain , edited by E. J. Hannan, P. R. Krishnaiah and M. M. Rao ( Amsterdam North-Holland ), pp. 25 – 83 .
   Google Scholar
• PAO , YOH-HAN , 1989 , Adaptive Pattern Recognition and Neural Networks ( Reading , Mass Addison-Wesley ).
   Google Scholar
• PARK , J. , and SANDBERG , I. W. , 1991 , Universal approximation using radial-basis-function networks . Neural Computation, 3 , 246 – 257 .
   Google Scholar
• POWELL , M. J. D. , 1987 , Radial basis function approximations to polynomials . Proceedings of the 12th Biennial Numerical Analysis Conference , Dundee , pp. 223 – 241 .
   Google Scholar
• PRIESTLEY , M. B. , 1980 , State-dependent models a general approach to non-linear time series analysis . Journal of Time Series Analysis , n1 n, 47 – 71 .
   Google Scholar
• RUMELHART , D. E. , HINTON , G. E. , and WILLIAMS , R. J. , 1986 , Learning internal representations by error propagation . Parallel Distributed Processing Explorations in the Micro-structure of Cognition , edited by D. E. Rumelhart and J. L. McClelland ( Cambridge , Mass MIT Press ), pp. 318 – 362 .
   Google Scholar
• SALOADO , M. E. , GOODWIN, G. C, and MIDDLETON , R. H. , 1988 , Modified least squares algorithm incorporating exponential resetting and forgetting . International Journal of Control , n47 n, 477 – 491 .
   Web of Science ®Google Scholar
• SIMMONS , G. F. , 1963 , Introduction to Topology and Modern Analysis ( New York McGraw-Hill ).
   Google Scholar
• SRIPADA , N. R. , and FISHER , D. G. , 1987 , Improved least squares identification . International Journal of Control , n46 n, 1889 – 1913 .
   Web of Science ®Google Scholar
• WEIOEND , A. S. , HUBERMAN , B. A. , and RUMELHART , D. E. , 1990 , Predicting the future a connectionist approach . International Journal of Neural Systems , n1 n, 193 – 209 .
   Google Scholar