A Discrete-Time System Adaptive Control Using Multiple Models and RBF Neural Networks

  • Jun-Yong Zhai
  • Shu-Min Fei
  • Kan-Jian Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3972)


A new control scheme using multiple models and RBF neural networks is developed in this paper. The proposed scheme consists of multiple feedback linearization controllers, which are based on the known nominal dynamics model and a compensating controller, which is based on RBF neural networks. The compensating controller is applied to improve the transient performance. The neural network is trained online based on Lyapunov theory and learning convergence is thus guaranteed. Simulation results are presented to demonstrate the validity of the proposed method.


Adaptive Control Multiple Model Lyapunov Theory IEEE Control System Magazine NARMAX Model 


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  1. 1.
    Chen, S., Billings, S.A.: Representation of Non-linear Systems: The NARMAX Model. Int. Journal of Control 49(3), 1013–1032 (1989)MATHMathSciNetGoogle Scholar
  2. 2.
    Narendra, K.S., Cheng, X.: Adaptive Control of Discrete-time Systems Using Multiple Models. IEEE Trans. Automatic Control 45(9), 1669–1686 (2000)MATHCrossRefGoogle Scholar
  3. 3.
    Narendra, K.S., Balakrishnan, J., Ciliz, M.K.: Adaptation and Learning Using Multiple Models, Switching, and Tuning. IEEE Control Systems Magazine 15(3), 37–51 (1995)CrossRefGoogle Scholar
  4. 4.
    Narendra, K.S., Balakrishnan, J.: Adaptive Control Using Multiple Models. IEEE Trans. Automatic Control 42(2), 171–187 (1997)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gang, F.: Position Control of A PM Stepper Motor Using Neural Networks. In: Proceedings of the 39th Conference on Decision and Control, Sydney, Australia, pp. 1766–1769 (2000)Google Scholar
  6. 6.
    Shamma, J.S., Athans, M.: Analysis of Gain Scheduled Control For Nonlinear Plants. IEEE Trans. Automatic Control 35(8), 898–907 (1990)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Matausek, M.R., Jeftenic, B.I., Miljkovic, D.M., et al.: Gain Scheduling Control of DC Motor Drive With Field Weakening. IEEE Trans. Industrial Electronics 43(1), 153–162 (1996)CrossRefGoogle Scholar
  8. 8.
    Zhai, J.Y., Fei, S.M.: Multiple Models Adaptive Control Based on RBF Neural Network Dynamic Compensation. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3498, pp. 36–41. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Morse, A.S., Mayne, D.Q., Goodwin, G.C.: Applications of Hysteresis Switching in Parameter Adaptive Control. IEEE Trans. Automatic Control 37(9), 1343–1354 (1992)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jun-Yong Zhai
    • 1
  • Shu-Min Fei
    • 1
  • Kan-Jian Zhang
    • 1
  1. 1.Research Institute of AutomationSoutheast UniversityNanjingChina

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