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
Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19, 716–723 (1974)
Atencia, M., Sandoval, G.: Gray box identification with hopfield neural networks. Rev. Inv. Oper. 25, 54–60 (2004)
Bhama, S., Singh, H.: Single layer neural network for linear system identification using gradient descent technique. IEEE Trans. Neural Netw. 4, 884–888 (1993)
Chu, S.R., Shoureshi, R., Tenorio, M.: Neural networks for system identification. IEEE Control Syst. Mag. 10, 31–34 (1990)
Haykin, S.: Neural Networks – A Comprehensive Foundation, 2nd edn. Prentice Hall, Upper Saddle River (1999)
Hopfield, J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)
Ljung, L.: System Identification – Theory for the User, 2nd edn. Prentice-Hall, Upper Saddle River (1999)
Mehrotra, K., Mohan, C., Ranka, S.: Elements of Artificial Neural Networks. MIT Press, Cambridge (1997)
Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Netw. 1, 1–27 (1990)
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)
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)
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)
Söderström, T., Stoica, P.: System Identification. Prentice Hall, Englewood Cliffs (1989)
Wellstead, P.E.: An instrumental product moment test for model order estimation. Automatica 14, 89–91 (1978)
Widrow, B., Lehr, M.A.: 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proc. IEEE 78, 1415–1442 (1990)
Woodside, C.M.: Estimation of the Order of Linear Systems. Automatica 7, 727–733 (1971)
Zhang, W.: System identification based on a generalized ADALINE neural network. In: Proceedings of the 2007 ACC, New York City, pp. 4792–4797 (2007)
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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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