A Robust Fuzzy Adaptive Control Algorithm for a Class of Nonlinear Systems

  • Sašo Blažič
  • Igor Škrjanc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7824)


The paper presents a general methodology of adaptive control based on soft computing models to deal with unknown plants. The problem of parameter estimation is solved using a direct approach, i.e., the controller parameters are adapted without explicitly estimating plant parameters. Thus, very simple adaptive and control laws are constructed within the Lyapunov stability framework. The proposed control ensures global stability of the overall system and convergence of the tracking error to a residual set that depends on the size of unmodelled dynamics. The generality of the approach is substantiated by Stone-Weierstrass theorem, which indicates that any continuous function can be approximated by fuzzy basis function expansion. The hallmarks of the approach are its simplicity and transparency. The paper shows the efficiency of the proposed approach on the control of a heat exchanger.


adaptive control fuzzy model Takagi-Sugeno model model-reference adaptive control 


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  1. 1.
    Abonyi, J., Andersen, H., Nagy, L., Szeifert, F.: Inverse fuzzy-process-model based direct adaptive control. Mathematics and Computers in Simulation 51(1-2), 119–132 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Blažič, S., Škrjanc, I., Matko, D.: Globally stable direct fuzzy model reference adaptive control. Fuzzy Sets and Systems 139(1), 3–33 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ge, S., Wang, J.: Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Transactions on Neural Networks 13(6), 1409–1419 (2002)CrossRefGoogle Scholar
  4. 4.
    Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall (1996)Google Scholar
  5. 5.
    Koo, K.M.: Stable adaptive fuzzy controller with time varying dead-zone. Fuzzy Sets and Systems 121 (2001)Google Scholar
  6. 6.
    Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks 1(1), 4–27 (1990)CrossRefGoogle Scholar
  7. 7.
    Narendra, K., Balakrishnan, J.: Adaptive control using multiple models. IEEE Transactions on Automatic Control 42(2), 171–187 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Precup, R.E., Doboli, S., Preitl, S.: Stability analysis and development of a class of fuzzy control systems. Engineering Applications of Artificial Intelligence 13(3), 237–247 (2000)CrossRefGoogle Scholar
  9. 9.
    Precup, R.E., Hellendoorn, H.: A survey on industrial applications of fuzzy control. Computers in Industry 62(3), 213–226 (2011)CrossRefGoogle Scholar
  10. 10.
    Richalet, J.: Industrial applications of model based predictive control. Automatica 29(5), 1251–1274 (1993)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Škrjanc, I., Matko, D.: Predictive functional control based on fuzzy model for heat-exchanger pilot plant. IEEE Transactions on Fuzzy Systems 8(6), 705–712 (2000)CrossRefGoogle Scholar
  12. 12.
    Spooner, J., Passino, K.: Stable adaptive control using fuzzy systems and neural networks. IEEE Transactions on Fuzzy Systems 4(3), 339–359 (1996)CrossRefGoogle Scholar
  13. 13.
    Tong, S., Li, Y.: Adaptive Fuzzy Output Feedback Tracking Backstepping Control of Strict-Feedback Nonlinear Systems With Unknown Dead Zones. IEEE Transactions on Fuzzy Systems 20(1), 168–180 (2012)CrossRefGoogle Scholar
  14. 14.
    Tong, S., Wang, T., Tang, J.T.: Fuzzy adaptive output tracking control of nonlinear systems. Fuzzy Sets and Systems 111 (2000)Google Scholar
  15. 15.
    Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Transactions on Fuzzy Systems 1 (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sašo Blažič
    • 1
  • Igor Škrjanc
    • 1
  1. 1.Faculty of Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenia

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