Advertisement

Journal of Zhejiang University-SCIENCE A

, Volume 7, Issue 2, pp 275–284 | Cite as

Nonlinear decoupling controller design based on least squares support vector regression

  • Wen Xiang-jun  (文香军)
  • Zhang Yu-nong  (张雨浓)
  • Yan Wei-wu  (阎威武)
  • Xu Xiao-ming  (许晓鸣)
Article

Abstract

Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control of a general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is unknown or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.

Key words

Support Vector Machine (SVM) Decoupling control Nonlinear system Generalized inverse system 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, F., Liu, C., 1994. Adaptively controlling nonlinear continuous-time systems using multiplayer neural networks. IEEE Transactions on Automatic Control, 39(6):1306–1310. [doi:10.1109/9.293202]CrossRefMATHGoogle Scholar
  2. Dai, X., Zhang, K., Zhang, T., Lu, X., 2004. ANN generalized inversion control of turbo generator governor. IEE Proceedings-Generation, Transmission and Distribution, 151(3):327–333. [doi:10.1049/ip-gtd:20040380]CrossRefGoogle Scholar
  3. Descusse, J., Moog, C., 1985. Decoupling with dynamic compensation for strong invertible affine nonlinear systems. International Journal of Control, 42(6):1387–1398.MathSciNetCrossRefMATHGoogle Scholar
  4. Godbole, D.N., Sastry, S.S., 1995. Approximate decoupling and asymptotic tracking for MIMO systems. IEEE Transactions on Automatic Control, 40(3):441–450. [doi:10.1109/9.376056]MathSciNetCrossRefMATHGoogle Scholar
  5. He, D., Dai, X., Wang, Q., 2002. Generalized ANN inverse control method. Control Theory and Applications, 19(1):34–40 (in Chinese).MathSciNetMATHGoogle Scholar
  6. Hirschorn, R.M., 1979. Invertibility of multivariable nonlinear control systems. IEEE Transactions on Automatic Control, 24(6):855–865. [doi:10.1109/TAC.1979.1102181]MathSciNetCrossRefMATHGoogle Scholar
  7. Kwok, J.T., 2000. The evidence framework applied to Support Vector Machines. IEEE Transaction on Neural Network, 11(5):1162–1173. [doi:10.1109/72.870047]CrossRefGoogle Scholar
  8. Mackay, D.J.C., 1992. Bayesian interpolation. Neural Computing, 4:415–447.CrossRefMATHGoogle Scholar
  9. Mackay, D.J.C., 1997. Probable network and plausible predictions—A review of practical Bayesian methods for supervised neural networks. Network Computation in Neural Systems, 6:1222–1267.Google Scholar
  10. Mercer, J., 1909. Functions of positive and negative type and their connection with the theory of integral equations. Transactions of the London Philosophical Society A, 209:415–446.CrossRefMATHGoogle Scholar
  11. Nguyen, D.H., Widrow, B., 1990. Neural networks for self-learning control systems. IEEE Control Systems Magazine, 10(3):18–23. [doi:10.1109/37.55119]CrossRefGoogle Scholar
  12. Nijmeijer, H., Schaft, A., 1990. Nonlinear Dynamical Control Systems. Springer-Verlag, New York.CrossRefMATHGoogle Scholar
  13. Suykens, J.A.K., 2001. Support vector machines: a nonlinear modelling and control perspective. European Journal of Control, 7(2-3):311–327.CrossRefMATHGoogle Scholar
  14. Suykens, J.A.K., Vandewalle, J., 2000. Recurrent least squares support vector machines. IEEE Transactions on Circuits and Systems, Part I, 47(7):1109–1114. [doi:10.1109/81.855471]CrossRefGoogle Scholar
  15. Suykens, J.A.K., Vandewalle, J., de Moor, B., 2001. Optimal control by least squares Support Vector Machines. Neural Networks, 14(1):23–35. [doi:10.1016/S0893-6080(00)00077-0]CrossRefGoogle Scholar
  16. Suykens, J.A.K., Gestel, T., de Brabanter, J., de Moor, B., Vandewalle, J., 2002. Least Squares Support Vector Machines. World Scientific, Singapore.CrossRefMATHGoogle Scholar
  17. vanGestel, T., Suykens, J.A.K., Baestaens, D., Lambrechts, A., Lanckriet, G., Vandaele, B., de Moor, B., 2001. Financial time series prediction using least squares support vector machines within the evidence framework. IEEE Transaction on Neural Network, 12(4):809–821. [doi:10.1109/72.935093]CrossRefGoogle Scholar
  18. vanGestel, T., Suykens, J.A.K., Lanckriet, G., Lambrechts, A., de Moor, B., Vandewalle, J., 2002. Bayesian framework for least squares Support Vector Machine classifiers, Gaussian processes and Kernel Fisher discriminant analysis. Neural Computation, 15(5):1115–1148. [doi:10.1162/089976602753633411]CrossRefMATHGoogle Scholar
  19. Vapnik, V., 1998. The Nature of Statistical Learning Theory. Springer-Verlag, New York.MATHGoogle Scholar
  20. Walach, E., Widrow, B., 1983. Adaptive Signal Processing for Adaptive Control. IFAC workshop on Adaptive Systems in Control and Signal Processing, San Francisco, CA.Google Scholar
  21. Yan, W., Shao, H., Wang, X., 2004. Soft sensing modelling based on Support Vector Machine and Bayesian model selection. Computers and Chemical Engineering, 28:1489–1498.CrossRefGoogle Scholar
  22. Zhang, Y., Wang, J., 2001. Recurrent neural networks for nonlinear output regulation. Automatica, 37:1161–1173. [doi:10.1016/S0005-1098(01)00092-9]MathSciNetCrossRefMATHGoogle Scholar
  23. Zhang, Y., Wang, J., 2002. Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment. IEEE Transactions on Neural Networks, 13(3):633–644. [doi:10.1109/TNN.2002.1000129]CrossRefGoogle Scholar
  24. Zhang, Y., Ge, S.S., 2003. A General Recurrent Neural Network work Model for Time-varying Matrix Inversion. The IEEE 42nd IEEE Conference on Decision and Control, p.6169-6174.Google Scholar
  25. Zhang, Y., Jiang, D., Wang, J. 2002. A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Transactions on Neural Networks, 13(5):1053–1063. [doi:10.1109/TNN.2002.1031938]CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Wen Xiang-jun  (文香军)
    • 1
  • Zhang Yu-nong  (张雨浓)
    • 2
  • Yan Wei-wu  (阎威武)
    • 1
  • Xu Xiao-ming  (许晓鸣)
    • 1
  1. 1.Department of Automatic ControlShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of Electronic and Electrical EngineeringUniversity of StrathclydeGlasgowUK

Personalised recommendations