Neural network-based NARX models in non-linear adaptive control

Andrzej Dzieliński

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 235-240
  • ISSN: 1641-876X

Abstract

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The applicability of approximate NARX models of non-linear dynamic systems is discussed. The models are obtained by a new version of Fourier analysis-based neural network also described in the paper. This constitutes a reformulation of a known method in a recursive manner, i.e. adapted to account for incoming data on-line. The method allows us to obtain an approximate model of the non-linear system. The estimation of the influence of the modelling error on the discrepancy between the model and real system outputs is given. Possible applications of this approach to the design of BIBO stable closed-loop control are proposed.

How to cite

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Dzieliński, Andrzej. "Neural network-based NARX models in non-linear adaptive control." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 235-240. <http://eudml.org/doc/207583>.

@article{Dzieliński2002,
abstract = {The applicability of approximate NARX models of non-linear dynamic systems is discussed. The models are obtained by a new version of Fourier analysis-based neural network also described in the paper. This constitutes a reformulation of a known method in a recursive manner, i.e. adapted to account for incoming data on-line. The method allows us to obtain an approximate model of the non-linear system. The estimation of the influence of the modelling error on the discrepancy between the model and real system outputs is given. Possible applications of this approach to the design of BIBO stable closed-loop control are proposed.},
author = {Dzieliński, Andrzej},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {adaptive control; neural networks; nonlinear systems},
language = {eng},
number = {2},
pages = {235-240},
title = {Neural network-based NARX models in non-linear adaptive control},
url = {http://eudml.org/doc/207583},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Dzieliński, Andrzej
TI - Neural network-based NARX models in non-linear adaptive control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 235
EP - 240
AB - The applicability of approximate NARX models of non-linear dynamic systems is discussed. The models are obtained by a new version of Fourier analysis-based neural network also described in the paper. This constitutes a reformulation of a known method in a recursive manner, i.e. adapted to account for incoming data on-line. The method allows us to obtain an approximate model of the non-linear system. The estimation of the influence of the modelling error on the discrepancy between the model and real system outputs is given. Possible applications of this approach to the design of BIBO stable closed-loop control are proposed.
LA - eng
KW - adaptive control; neural networks; nonlinear systems
UR - http://eudml.org/doc/207583
ER -

References

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  3. Dzieliński A. (1999): Bibo Stability of Approximate NARX Models. - Proc. Amer. Contr. Conf., ACC'99, San Diego, USA, pp. 4000-4002. 
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  6. Leontaritis I.J. and Billings S.A. (1985): Input-output parametric models for non-linear systems. Part I: Deterministic non-linear systems. - Int. J. Contr., Vol. 41, No. 2, pp. 303-328. Zbl0569.93011
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  11. Sanner R.M. and Slotine J.-J.E. (1992): Gaussian Networks for Direct Adaptive Control. - IEEE Trans. Neural Netw., Vol. 3, No. 6, pp. 837-863. 
  12. Stein E.M. and Weiss G. (1971): Introduction to Fourier Analysis on Euclidean Spaces. - Princeton: Princeton University Press. Zbl0232.42007
  13. Stroud A.H. (1971): Approximate Calculation of Multiple Integrals. - Englewood Cliffs: Prentice-Hall. Zbl0379.65013
  14. Tikhonov A.N. and Arsenin V.Y. (1977): Solution of Ill-posed Problems. - New York: Wiley. Zbl0354.65028
  15. Żbikowski R. and Dzieliński A. (1996): Non-uniform Sampling Approachto Control Systems Modelling with Feedforward Networks, In: Neural Adaptive Control Technology (R. Żbikowski and K.J. Hunt, Eds.). - Singapore, London: World Scientific, pp. 71-112. 

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