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Input Dimension Determination of Linear Feedback Neural Network Applied for System Identification of Linear Systems

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Advances in Neural Networks - ISNN 2017 (ISNN 2017)

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Abstract

In the application of a linear neural network (LNN) to linear system identification and parameter estimation, it is important to determine the input dimension of the LNN so that the identification can be performed efficiently. In the LNN for linear system identification, both the input and output data are taken as input of the LNN. The output data are delayed and are fed-back to input of the LNN. The input dimension determination is to determine the right number of past inputs should be applied to its input and the right number of past outputs should be fed-back to its input also. The sampled input and output data are used to train the LNN. The performance errors are collected during training and are used in the evaluation by Akaike’s Information Criterion to determine the input dimension. The advantage of LNN method is its simplicity and effectiveness. Satisfactory results from simulation are provided to show the effectiveness of the proposed algorithm.

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References

  1. Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19, 716–723 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. Atencia, M., Sandoval, G.: Gray box identification with hopfield neural networks. Rev. Inv. Oper. 25, 54–60 (2004)

    MathSciNet  MATH  Google Scholar 

  3. Bhama, S., Singh, H.: Single layer neural network for linear system identification using gradient descent technique. IEEE Trans. Neural Netw. 4, 884–888 (1993)

    Article  Google Scholar 

  4. Chu, S.R., Shoureshi, R., Tenorio, M.: Neural networks for system identification. IEEE Control Syst. Mag. 10, 31–34 (1990)

    Article  Google Scholar 

  5. Haykin, S.: Neural Networks – A Comprehensive Foundation, 2nd edn. Prentice Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  6. Hopfield, J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  7. Ljung, L.: System Identification – Theory for the User, 2nd edn. Prentice-Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  8. Mehrotra, K., Mohan, C., Ranka, S.: Elements of Artificial Neural Networks. MIT Press, Cambridge (1997)

    MATH  Google Scholar 

  9. Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Netw. 1, 1–27 (1990)

    Article  Google Scholar 

  10. Qin, S.Z., Su, H.T., McAvoy, T.J.: Comparison of four neural net learning methods for dynamic system identification. IEEE Trans. Neural Netw. 2, 52–262 (1992)

    Google Scholar 

  11. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. I, MIT Press, Cambridge (1986)

    Google Scholar 

  12. Sjöberg, J., Hjalmerson, H., Ljung, L.: Neural networks in system identification. In: The 10th IFAC Symposium on SYSID, Copenhagen, Denmark, vol. 2, pp. 49–71 (1994)

    Google Scholar 

  13. Söderström, T., Stoica, P.: System Identification. Prentice Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  14. Wellstead, P.E.: An instrumental product moment test for model order estimation. Automatica 14, 89–91 (1978)

    Article  Google Scholar 

  15. Widrow, B., Lehr, M.A.: 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proc. IEEE 78, 1415–1442 (1990)

    Article  Google Scholar 

  16. Woodside, C.M.: Estimation of the Order of Linear Systems. Automatica 7, 727–733 (1971)

    Article  MATH  Google Scholar 

  17. Zhang, W.: System identification based on a generalized ADALINE neural network. In: Proceedings of the 2007 ACC, New York City, pp. 4792–4797 (2007)

    Google Scholar 

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Correspondence to Wenle Zhang .

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Zhang, W. (2017). Input Dimension Determination of Linear Feedback Neural Network Applied for System Identification of Linear Systems. In: Cong, F., Leung, A., Wei, Q. (eds) Advances in Neural Networks - ISNN 2017. ISNN 2017. Lecture Notes in Computer Science(), vol 10262. Springer, Cham. https://doi.org/10.1007/978-3-319-59081-3_47

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  • DOI: https://doi.org/10.1007/978-3-319-59081-3_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59080-6

  • Online ISBN: 978-3-319-59081-3

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