Adaptive Neural Control for a Class of MIMO Non-linear Systems with Guaranteed Transient Performance

  • Tingliang Hu
  • Jihong Zhu
  • Zengqi Sun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3972)


A robust adaptive control scheme is presented for a class of uncertain continuous-time multi-input multi-output (MIMO) nonlinear systems. Within these schemes, multiple multi-layer neural networks are employed to approximate the uncertainties of the plant’s nonlinear functions and robustifying control term is used to compensate for approximation errors. All parameter adaptive laws and robustifying control term are derived based on Lyapunov stability analysis so that all the signals in the closed loop are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the output is proven to converge to a small neighborhood of zero. While the relationships among the control parameters, adaptive gains and robust gains are established to guarantee the transient performance of the closed loop system.


Close Loop System Tracking Error Radial Basis Function Neural Network Adaptive Gain Neural Network Weight 
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.
    Isidori, A.: Nonlinear Control System. Springer, Berlin (1989)Google Scholar
  2. 2.
    Sastry, S.S., Isidori, A.: Adaptive Control of Linearizable Systems. IEEE Trans. Automat. Contr. 34, 1123–1131 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kanellakopoulos, I., Kokotovic, P.V., Morse, A.S.: Systematic Design of Adaptive Controllers for Feedback Linearizable Systems. IEEE Trans. Automat. Contr. 36, 1241–1253 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Slotine, J.-J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)zbMATHGoogle Scholar
  5. 5.
    Sanner, R., Slotine, J.-J.E.: Gaussian Networks for Direct Adaptive Control. IEEE Trans. Neural Networks 3, 837–863 (1992)CrossRefGoogle Scholar
  6. 6.
    Polycarpou, M.M.: Stable Adaptive Neural Control for Nonlinear Systems. IEEE Trans. Automat. Contr. 41, 447–450 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Rovithakis, G.A., Christodulou, M.A.: Neural Adaptive Regulation of Unknown Nonlinear Dynamical Systems. IEEE Trans. Syst., Man, Cybern. B 27, 810–822 (1997)CrossRefGoogle Scholar
  8. 8.
    Xu, H., Ioannou, P.A.: Robust Adaptive Control for a Class of MIMO Nonlinear Systems With Guaranteed Error Bounds. IEEE Trans. Automat. Contr. 48, 728–742 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Ge, S.S., Wang, C.: Adaptive Neural Control of Uncertain MIMO Nonlinear Systems. IEEE Trans. Neural Networks 15, 674–692 (2004)CrossRefGoogle Scholar
  10. 10.
    Lewis, F.L., Liu, K., Yesildirek, A.: Neural Net Robot Controller with Guaranteed Tracking Performance. IEEE Trans. Neural Networks 6, 703–715 (1995)CrossRefGoogle Scholar
  11. 11.
    Cheny, S.-C., Chenz, W.-L.: Adaptive Radial Basis Function Neural Network Control with Variable Variance Parameters. Int. Journal of Systems Science 2, 413–424 (2001)CrossRefGoogle Scholar
  12. 12.
    Spooner, J.T., Passino, K.M.: Stable Adaptive Control Using Fuzzy Systems and Neural Networks. IEEE Trans. Fuzzy Syst. 4, 339–359 (1996)CrossRefGoogle Scholar
  13. 13.
    Zhang, T., Ge, S.S., Hang, C.C.: Design and Performance Analysis of a Direct Adaptive Controller for Nonlinear Systems. Automatica 35, 1809–1817 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Park, J.H., Huh, S.H., Kim, S.H., Seo, S.J., Park, G.T.: Direct Adaptive Controller for Nonaffion Nonlinear Systems Using Self-Structuring Neural Networks. IEEE Trans. Neural Networks 16, 414–422 (2005)CrossRefGoogle Scholar
  15. 15.
    Narendra, K.S., Annaswamy, A.M.: A New Adaptive Law for Robust Adaptation without Persistent Excitation. IEEE Trans. Automat. Contr. 32, 134–145 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Taylor, D.: Composite Control of Direct-drive Robots. In: Proceedings of the IEEE Conference on Decision and Control, pp. 1670–1675 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tingliang Hu
    • 1
  • Jihong Zhu
    • 1
  • Zengqi Sun
    • 1
  1. 1.State Key Lab of Intelligent Technology and Systems, Department of Computer Science and TechnologyTsinghua UniversityBeijingChina

Personalised recommendations