Advertisement

Least Squares Support Vector Machine Based Partially Linear Model Identification

  • You-Feng Li
  • Li-Juan Li
  • Hong-Ye Su
  • Jian Chu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4113)

Abstract

A nonlinear identification method was proposed for a class of partially linear models (PLM) which consist of a linear component summed with a nonlinear component in nonlinear ARX form. The method extends the standard least squares support vector machine (LSSVM) by replacing the equality constraint in the standard LSSVM with a PLM model. To guarantee the uniqueness of the linear coefficients, we imposed an additional explicit constraint on the feature map instead of an implicit constraint on the regressor vectors. Therefore the resulting PLM is a generalized version of the original one. Two examples show the effectiveness of the presented method.

Keywords

Support Vector Machine Mean Square Error Model Predictive Control Partially Linear Model Implicit Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Engle, R.F., Granger, C.W.J., Rice, J., Weiss, A.: Semiparametric Estimates of The Relation Between Weather and Electricity Sales. J. Amer. Statist. Assoc. 81, 310–320 (1986)CrossRefGoogle Scholar
  2. 2.
    Espinoza, M., Suykens, J.A.K., De Moor, B.: Kernel Based Partially Linear Models and Nonlinear Identification. IEEE Transactions on Automatic Control 50, 1602–1606 (2005)CrossRefGoogle Scholar
  3. 3.
    Goethals, I., Pelckmans, K., Suykens, J.A.K., De Moor, B.: Subspce Identification of Hammerstein Systems Using Least Squares Support Vector Machines. IEEE Transactions on Automatic Control 50, 1509–1519 (2005)CrossRefGoogle Scholar
  4. 4.
    Qin, S.J., Badgwell, T.A.: Survey of Industrial Model Predictive Control Technology. Control Engineering Practice 11, 733–764 (2003)CrossRefGoogle Scholar
  5. 5.
    Schoukens, J., Nemeth, J.G., Crama, P., Rolain, Y., Pintelon, R.: Fast Approximate Identification of Nonlinear Systems. Automatica 39, 1267–1274 (2003)MATHMathSciNetGoogle Scholar
  6. 6.
    Sjöberg, J., Zhang, Q., Ljung, L., Benveniste, A., Deylon, B., Glorennec, P., Hjalmarsson, H., Juditsky, A.: Nonlinear Black-box Modeling in System Identification: A Unified Overview. Automatica 31, 1691–1724 (1995)MATHCrossRefGoogle Scholar
  7. 7.
    Suykens, J.A.K., De Brabanter, J., Lukas, L., Vandewalle, J.: Weighted Least Squares Support Vector Machines: Robustness and Sparse Approximation. Neurocomputing 48, 85–105 (2002)MATHCrossRefGoogle Scholar
  8. 8.
    Suykens, J.A.K., Vandewalle, J., De Moor, B.: Optimal Control By Least Squares Support Vector Machines. Neural Networks 14, 23–35 (2001)CrossRefGoogle Scholar
  9. 9.
    Van Gestel, T., Suykens, J.A.K., De Moor, B., Vandewalle, J.: Bayesian Inference for LS-SVMs on Large Data Sets Using the Nyström Method. In: Proceedings of the 2002 International Joint Conference on Neural Networks, vol. 3, pp. 2779–2784 (2002)Google Scholar
  10. 10.
    Verdult, V., Verhaegen, M.: Kernel Methods for Subspace Identification of Multivariable LPV and Bilinear Systems. Automatica 41, 1557–1565 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhao, H., Guiver, J., Sentoni, G.: An Identifcation Approach to Nonlinear State Space Model for Industrial Multivariable Model Predictive Control. In: Proceedings of the American Control Conference, pp. 796–800 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • You-Feng Li
    • 1
  • Li-Juan Li
    • 1
  • Hong-Ye Su
    • 1
  • Jian Chu
    • 1
  1. 1.National Key Laboratory of Industrial Control Technology, Institute of Advanced Process ControlZhejiang UniversityHangzhouP.R. China

Personalised recommendations