H ∞  Neural Networks Control for Uncertain Nonlinear Switched Impulsive Systems

  • Fei Long
  • Shumin Fei
  • Zhumu Fu
  • Shiyou Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4234)


Based on RBF (radial basis function) neural network, an adaptive neural network feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy in this paper. Impulsive controller is designed to attenuate effect of switching impulse. The RBF neural net-work is used to compensate adaptively for the unknown nonlinear part of switched impulsive systems, and the approximation error of RBF neural net-work is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Under all admissible switching law, impulsive controller and adaptive neural network feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall switched impulsive system.


Tracking Error Impulsive System Disturbance Attenuation Neural Network Control Adaptive Neural Network 
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  1. 1.
    Liu, C., Chen, F.: Adaptive Control of Nonlinear Continuous Systems Using Neural Network—General Relative Degree and MIMO Case. International Journal of Control 58, 317–335 (1993)CrossRefMATHMathSciNetGoogle 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.
    Sridhar, S., Hassan, K.K.: Output Feedback Control of Nonlinear Systems Using RBF Neural Networks. IEEE Trans. Neural Network 11, 69–79 (2000)CrossRefGoogle Scholar
  7. 7.
    Levin, A.U., Narendra, K.S.: Control of Nonlinear Dynamical Systems Using Neural Networks-Part II: Observability, Identification, and Control. IEEE Trans. Neural Networks 7, 30–42 (1996)CrossRefGoogle Scholar
  8. 8.
    Narendra, K.S., Parthasarathy, K.: Identification and Control of Dynamic Systems Using Neural Networks. IEEE Trans. Neural Networks 1, 4–27 (1990)CrossRefGoogle Scholar
  9. 9.
    Ge, S.S., et al.: A Direct Method for Robust Adaptive Nonlinear Control with Guaranteed Transient Performance. System Control Letter 37, 275–284 (1999)CrossRefMATHGoogle Scholar
  10. 10.
    Lewis, F.L., et al.: Multilayer Neural-Net Robot Controller with Guaranteed Tracking Performance. IEEE Trans. Neural Networks 7, 388–398 (1999)CrossRefGoogle Scholar
  11. 11.
    Polycarpou, M.M.: Stable Adaptive Neural Control Scheme for Nonlinear Systems. IEEE Trans. Automatic Control 41, 447–450 (1996)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Ge, S.S., et al.: Adaptive Neural Networks Control of Robotic Manipulators. World Scientific, Singapore (1998)Google Scholar
  13. 13.
    Ge, S.S., et al.: Stable Adaptive Neural Network Control. Kluwer, Norwell (2001)Google Scholar
  14. 14.
    Long, F., Fei, S.M.: State Feedback Control for a Class of Switched Nonlinear Systems Based on RBF Neural Networks. In: Proc. 23rd Chinese Control Conference, vol. 2, pp. 1611–1614 (2004)Google Scholar
  15. 15.
    Long, F., Fei, S.M., Zheng, S.Y.: H-infinity Control for Switched Nonlinear Systems Based on RBF Neural Networks. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3498, pp. 54–59. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Long, F., Fei, S.M., Fu, Z.M., Zheng, S.Y.: Adaptive Neural Network Control for Switched System with Unknown Nonlinear Part by Using Backstepping Approach: SISO Case. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3972, pp. 842–848. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Long, F., Fei, S.M., Zheng, S.Y.: Adaptive Control for A Class of Switched Nonlinear Systems Based on RBF Neural Networks. International Journal of Hybrid Systems 4, 369–380 (2004)Google Scholar
  18. 18.
    Xu, H.L., Liu, X.Z., Teo, K.L.: Robust H-Infinity Stabilization with Definite Attendance of an Uncertain Impulsive Switched System. ANZIAM Journal 46, 471–484 (2005)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Wang, Y.J., Xie, G.M., Wang, L.: Reachability and Controllability of Switched Linear Systems with State Jumps. In: Proceedings of the IEEE international conference on systems, man and cybernetics, vol. 1-5, pp. 672–677 (2003)Google Scholar
  20. 20.
    Xie, G.M., Wang, L.: Reachability of Switched Linear Impulsive Systems. In: Proceedings of the IEEE Conference on Decision and Control, vol. 6, pp. 6271–6276 (2003)Google Scholar
  21. 21.
    Zhang, H.T., Liu, X.Z.: Robust H-Infinity Control on Impulsive Switched Systems with Disturbance. Control Theory and Applications 21, 261–266 (2004)MATHGoogle Scholar
  22. 22.
    Xie, G.M., Wang, L.: Necessary and Sufficient Conditions for Controllability and Ob-servability of Switched Impulsive Control Systems. IEEE Transactions on Automatic Control 49, 960–966 (2004)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Guan, Z.H., Hill, D.J., Shen, X.: On Hybrid Impulsive and Switching Systems and Application to Nonlinear Control. IEEE Trans. on Automatic Control 50, 1058–1062 (2005)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Long, F., Fei, S.M.: Tracking Stabilization for A Class of Switched Impulsive Systems Using RBF Neural Networks. Dynamics of Continuous Discrete and Impulsive Systems—Series A: Mathematical Analysis 13 (Part 1, suppl. S), 356–363 (2006)MathSciNetGoogle Scholar
  25. 25.
    Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice Hall, New York (1994)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fei Long
    • 1
    • 2
  • Shumin Fei
    • 2
  • Zhumu Fu
    • 2
  • Shiyou Zheng
    • 2
  1. 1.School of Informational EngineeringGuizhou UniversityGuiyangChina
  2. 2.Department of Automatic ControlSoutheast UniversityNanjingChina

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