H-Infinity Control for Switched Nonlinear Systems Based on RBF Neural Networks

  • Fei Long
  • Shumin Fei
  • Shiyou Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3498)


Sub-controller and switching strategy based on RBF neural network are presented for a class of switched nonlinear systems in this paper. Sub-controller consists of equivalent controller and H-infinity controller. RBF neural network is used to approximate the unknown part of switched nonlinear systems, and the approximation errors of the RBF neural networks are introduced to the adaptive law in order to improve the performance of the whole systems. Sub-controller and switching strategy are designed to guarantee asymptotic stability of the output tracking error and to attenuate the effect of the external disturbance and approximation errors to a given level.


Radial Basis Function Radial Basis Function Neural Network Radial Basis Function Network Switching Strategy Uncertain Nonlinear System 
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.
    Liu, C., Chen, F.: Adaptive Control of Nonlinear Continuous Systems Using Neural Network-General Relative Degree and MIMO Case. Int. J. Control 58, 317–335 (1993)zbMATHCrossRefGoogle Scholar
  2. 2.
    Narendrk, K.S., Mukhopadhyay, S.: Adaptive Control of Nonlinear Multivariable System Using Neural Network. Neural Network 7, 737–752 (1994)CrossRefGoogle Scholar
  3. 3.
    Liu, G.P., et al.: Variable Neural Networks for Adaptive Control of Nonlinear Systems. IEEE Trans Systems, man, Cybermetics-Part C 29, 34–43 (1999)CrossRefGoogle Scholar
  4. 4.
    Patino, H.D., Liu, D.: Neural Network-based Model Reference Adaptive Control Systems. IEEE Trans Systems, man, Cybermetics-Part B 30, 198–204 (2001)CrossRefGoogle Scholar
  5. 5.
    Sanner, R., Slotine, J.J.: Gaussian Networks for Direct Adaptive Control. IEEE Trans on Neural Networks 3, 837–864 (1992)CrossRefGoogle Scholar
  6. 6.
    Seshagiri, S., Hassan, K.K.: Output Feedback Control of Nonlinear Systems Using RBF Neural Networks. IEEE Trans On Neural Network 11, 69–79 (2000)CrossRefGoogle Scholar
  7. 7.
    Chen, M., et al.: Adaptive H ∞  Control For A Class Of Uncertain Nonlinear Systems Based On RBF Neural Networks. Control Theory & Applications 20, 27–32 (2003)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Ding, G., et al.: H ∞  Control Of Uncertain Nonlinear Systems Based On Neural Network. Control and Decision 12, 571–575 (1997)Google Scholar
  9. 9.
    Levin, A.U., Narendra, K.S.: Control of Nonlinear Dynamical Systems Using Neural Networks-Part II: Observability, Identification, and Control. IEEE Trans. On Neural Networks 7, 30–42 (1996)CrossRefGoogle Scholar
  10. 10.
    Narendra, K.S., Parthasarathy, K.: Identification and Control of Dynamic Systems Using Neural Networks. IEEE Trans. On Neural Networks 1, 4–27 (1990)CrossRefGoogle Scholar
  11. 11.
    Ge, S.S., et al.: A Direct Method for Robust Adaptive Nonlinear Control with Guaranteed Transient Performance. System Control Lett. 37, 275–284 (1999)zbMATHCrossRefGoogle Scholar
  12. 12.
    Lewis, F.L., et al.: Multilayer Neural-net Robot Controller with Guaranteed Tracking Performance. IEEE Trans. On Neural Networks 7, 388–398 (1996)CrossRefGoogle Scholar
  13. 13.
    Polycarpou, M.M.: Stable Adaptive Neural Control Scheme for Nonlinear Systems. IEEE Trans. Automat. Contr. 41, 447–450 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ge, S.S., et al.: Adaptive Neural Network Control of Robotic Manipulators. World Scientific, Singapore (1998)Google Scholar
  15. 15.
    Ge, S.S., et al.: Stable Adaptive Neural Network Control. Kluwer, Norwell (2001)Google Scholar
  16. 16.
    Long, F., Fei, S.: State Feedback Control for a Class of Switched Nonlinear Systems Based on RBF Neural Networks. In: Proc. 23rd Chinese Control Congress, Wuxi, China, pp. 1611–1614 (2004)Google Scholar
  17. 17.
    Isidori, A.: Nonlinear Control Systems, 2nd edn. Springer, New York (1995)zbMATHGoogle Scholar
  18. 18.
    Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice Hall, New York (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Fei Long
    • 1
  • Shumin Fei
    • 1
  • Shiyou Zheng
    • 1
  1. 1.Department of Automatic ControlSoutheast UniversityNanjingChina

Personalised recommendations