Sequential Support Vector Machine Control of Nonlinear Systems by State Feedback

  • Zonghai Sun
  • Youxian Sun
  • Xuhua Yang
  • Yongqiang Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3498)


Support vector machine is a new and promising technique for pattern classification and regression estimation. The training of support vector machine is characterized by a convex optimization problem, which involves the determination of a few additional tuning parameters. Moreover, the model complexity follows from that of this convex optimization problem. In this paper we introduce the sequential support vector machine for the regression estimation. The support vector machine is trained by the Kalman filter and particle filter respectively and then we design a controller based on the sequential support vector machine. Support vector machine controller is designed in the state feedback control of nonaffine nonlinear systems. The results of simulation demonstrate that the sequential training algorithms of support vector machine are effective and sequential support vector machine controller can achieve a satisfactory performance.


Support Vector Machine Kalman Filter State Feedback Particle Filter Extended Kalman Filter 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Vapnik, V.N.: Statistical Learning Theory. John Wiley and Sons, New York (1998)zbMATHGoogle Scholar
  2. 2.
    de Freitas, J.F.G., Niranjan, M., Gee, A.H., Doucet, A.: Sequential Monte Carlo Methods to Train Neural Network Models. Neural Computation 12, 955–993 (2000)CrossRefGoogle Scholar
  3. 3.
    Kalman, R.E., Bucy, R.S.: New Results of in Linear Filtering and Prediction Theory. Transaction of the ASME (Journal of Basic Engineering) 83, 95–108 (1961)MathSciNetGoogle Scholar
  4. 4.
    Storvik, G.: Particle Filters in State Space Models with the Presence of Unknown Static Parameters. IEEE Transactions on Signal Processing 50, 281–289 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Doucet, A., de Freitas, N., Murphy, K., Russell, S.: Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks. In: Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, Stanford, pp. 176–183 (2000)Google Scholar
  6. 6.
    Liu, S., Chen, R.: Sequential Monte Carlo Methods for Dynamic Systems. Journal of the American Statistical Association 93, 1032–1044 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Crisan, D., Doucet, A.: A Survey of Convergence Results on Particle Filtering Methods or Practitioners. IEEE Transactions on Signal Processing 50, 736–746 (2002)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Sun, Z.: Study on Support Vector Machine and Its Application in Control. PhD. Thesis, Zhejiang University, Hangzhou, China (2003)Google Scholar
  9. 9.
    Arulampalam, S., Maskell, S., Gordon, N., Clapp, T.: A Tutorial on Particle Filters for On-Line Nonlinear /Non-Gaussian Bayesian Tracking. IEEE Trans. Signal Process. 50, 174–189 (2002)CrossRefGoogle Scholar
  10. 10.
    Ge, S.S., Hang, C.C., Zhang, T.: Adaptive Neural Network Control of Nonlinear Systems by State and Output Feedback. IEEE Trans. SMC-part B: Cybernetics 29, 818–828 (1999)CrossRefGoogle Scholar
  11. 11.
    Calise, A.J., Hovakimyan, N., Idan, M.: Adaptive Output Feedback Control of Nonlinear Systems Using Neural Networks. Automatica 37, 1201–1211 (2001)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Zonghai Sun
    • 1
  • Youxian Sun
    • 1
  • Xuhua Yang
    • 2
  • Yongqiang Wang
    • 1
  1. 1.National Laboratory of Industrial Control TechnologyZhejiang UniversityHangzhouChina
  2. 2.College of Information EngineeringZhejiang University of TechnologyHangzhouChina

Personalised recommendations