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Original Articles

Representations of non-linear systems: the NARMAX model

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Pages 1013-1032 | Received 20 Apr 1988, Published online: 09 Apr 2008

References

  • Billings , S. A. 1986 , Introduction to nonlinear systems analysis and identification , Signal Processing for Control , Godfrey K. and Jones P. ( Berlin : Springer-Verlag ), pp. 261 – 294 .
  • Billings , S. A. and Chen , S. 1989 . Int. J. Systems Sci. , 20 : 467
  • Billings , S. A , Chen , S. , and Backhouse , R. J. 1989 , The identification of linear and nonlinear models of a turbocharged automotive diesel engine . Mech. Systems Signal Process. , to be published .
  • Billings , S. A. , and Fadzil , M. B. 1985 , The practical identification of systems with nonlinearities . Proc. 7th IFAC Symp. on Identification and System Parameter Estimation , York , U.K , pp. 155 – 160 .
  • Billings , S. A. , Fadzil , M. B. , Sulley , J. and Johnson , P. M. 1988a . Identification of a nonlinear difference equation model of an industrial diesel generator . Mech. Systems Signal Process , 2 : 59
  • Billings , S. A. , Korenberg , M. J. and Chen , S. 1988b . Int. J. Systems Sci. , 19 : 1559
  • Billings , S. A. , and Leontaritis , I. J. 1982 , Parameter estimation techniques for nonlinear systems . Proc. 6th IFAC Symposium on Identification and System Parameter Estimation , Washington , DC , pp. 505 – 510 .
  • Billings , S. A. and Voon , W. S. F . 1984 . Int. J. Systems Sci. , 15 : 601
  • Billings , S. A. and Voon , W. S. F. 1986 . Int. J. Control , 44 : 803
  • Bussgang , J. J , Ehrman , L and Graham , J. W . 1974 . Proc. Inst. elect. electron. Engrs , 62 : 1088
  • Chen , S , and Billings , S. A. 1988a , Int. J. Control , 47 , 309 ; 1988b, Recursive maximum likelihood identification of a nonlinear output-affine model. Ibid., 48, 1605; 1989, A recursive prediction error parameter estimator for nonlinear models. Ibid., 49, 569 .
  • Dang Van Mien , H. and Normand-Cyrot , D. 1984 . Automatica , 20 : 175
  • Dieudonné , J. 1960 . Foundations of Modern Analysis , New York : Academic Press .
  • España , M. and Landau , I. D. 1978 . Automatica , 14 : 345
  • Fliess , M. , and Normand-Cyrot , D. 1982 , On the approximation of nonlinear systems by some simple state-space models . Proc. 6th IFAC Symposium on Identification and System Parameter Estimation , Washington , DC , pp. 511 – 514 .
  • Granger , C. W. J. and Andersen , A. P. 1978 . An Introduction to Bilinear Time Series Models , Göttingen : Vandenhoeck and Ruprecht .
  • Hammer , J. 1984 . Int. J. Control , 40 : 1
  • Korenberg , M. J. , Billings , S. A. , Liu , Y. P and McIlroy , P J. 1988 . Int. J. Control , 48 : 193
  • Leontaritis , I. J. , and Billings , S. A. 1985 , Int. J. Control , 41 , 303 ; 1988, Int. J. Systems Sci., 19, 519 .
  • Ljung , L. 1987 . System Identification: Theory and User , Englewood Cliffs, NJ : Prentice Hall .
  • Ljung , L. and Söderström , T. 1983 . Theory and Practice of Recursive Identification , Cambridge, Mass : MIT Press .
  • Marmarelis , P Z. and Marmarelis , V. Z. 1978 . Analysis of Physiological Systems: The White-Noise Approach , New York : Plenum Press .
  • Mohler , R. R. 1973 . Bilinear Control Processes , New York : Academic Press) .
  • Neyran , B. , Thomasset , D. , and Dufour , J. 1987 , Proc. Instn elect. Engrs, Pt D , 134 , 89
  • Ozaki , T. 1985 , Non-linear time series models and dynamical systems , Handbook of Statistics , Vol. 5 , Time Series in the Time Domain , Hannan E. J. , Krishnaiah P. R. and Rao M. M. ( Amsterdam : North-Holland ), pp. 25 – 83 .
  • Potts , R. B. 1982 . Nonlinear Anal. Theory. Methods Applic. , 6 : 659
  • Rugh , W. J. 1981 . Nonlinear System Theory: The Volterra/Wiener Approach , Baltimore, Md : Johns Hopkins University Press .
  • Schetzen , M. 1980 . The Volterra and Wiener Theories of Nonlinear Systems , New York : John Wiley .
  • Simmons , G. F. 1963 . Introduction to Topology and Modern Analysis , New York : McGraw-Hill .
  • Sontag , E. D. 1979a , I.E.E.E. Trans. Circuits Systems , 26 , 342 ; 1979b, Polynomial response maps. Lecture Notes in Control and Information Sciences 13 (Berlin: Springer-Verlag) .

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