Synergetic Adaptive Fuzzy Control for a Class of Nonlinear Discrete-time Systems

  • Boukhalfa AbdelouahebEmail author
  • Khaber Farid
  • Essounbouli Najib
Regular Papers Intelligent Control and Applications


In this paper, a discrete-time adaptive fuzzy synergetic controller for a class of uncertain nonlinear dynamic systems is developed. Nonlinear systems, with configurations and parameters that fluctuate with time require a fully nonlinear model and a discrete-time adaptive control scheme for a practical operating environment. Therefore, an adaptive controller, which considers the nonlinear nature of the plant and adapts its parameters to changes in the environment is necessary and is addressed in this work. Depending on the Lyapunov synthesis, fuzzy sets universal approximation properties are used in a discrete adaptive scheme to approximate the nonlinear system while synergetic control guarantees robustness and the use of a chatter free discrete-time control law which makes the controller easy to implement. A simulation results of a real world example are indicated, to show the effectiveness of the proposed method.


Adaptive controller adaptive fuzzy synergetic controller discrete-time nonlinear system Lyapunov synthesis synergetic control theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. F. Ho, Y. K. Wong, and A. B. Rad, “Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems,” Simulation Modeling Practice and Theory, vol. 17, no. 7, pp. 1119–1210, August 2009.CrossRefGoogle Scholar
  2. [2]
    P. J. Olver and C. Shakiban, “Indirect adaptive fuzzy control for a class of nonlinear discrete-time system,” Applied Linear Algebra, 2005.Google Scholar
  3. [3]
    B. Erginer and E. Altuğ, “Design and implementation of a hybrid fuzzy logic controller for a quadrotor VTOL vehicle,” International Journal of Control, Automation, and Systems, vol. 10, no. 1, pp. 61–70, 2012.CrossRefGoogle Scholar
  4. [4]
    N. Sun, Y.Wu, Y. Fang, and H. Chen, “Nonlinear antiswing control for crane systems with double-pendulum swing effects and uncertain parameters: design and experiments,” IEEE Transactions on Automation Science and Engineering, vol. PP, no. 99, pp. 1–10, 2017.Google Scholar
  5. [5]
    L. Yu, S. Fei, and X. Li, “RBF neural networks-based robust adaptive tracking control for switched uncertain nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 10, no. 2, pp. 437–443, 2012.CrossRefGoogle Scholar
  6. [6]
    D. Bu, W. Sun, H. Yu, C. Wang, and H. Zhang, “Adaptive robust control based on RBF neural networks for duct cleaning robot,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 1–13, 2015.Google Scholar
  7. [7]
    Y. Li, S. Tong, L. Liu, and G. Feng, “Adaptive outputfeedback control design with prescribed performance for switched nonlinear systems,” Automatica, vol. 80, pp. 225–231, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    O. Roeva and T. Slavov, “PID controller tuning based on metaheuristic algorithms for bioprocess control,” Biotechnology & Biotechnological Equipment, vol. 26, no. 5, pp. 3267–3277, 2012.CrossRefGoogle Scholar
  9. [9]
    Y. Li, S. Sui, and S. Tong, “Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics,” IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 403–414, 2017.Google Scholar
  10. [10]
    C. Wu, J. Liu, Y. Xiong, and L. Wu, “Observer-based adaptive fault-tolerant tracking control of nonlinear nonstrictfeedback systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. PP, no. 99, pp. 1–12, 2017.Google Scholar
  11. [11]
    N. Sun, Y. Fang, H. Chen, and B. Lu, “Amplitude-saturated nonlinear output feedback antiswing control for underactuated cranes with double-pendulum cargo dynamics,” IEEE Transactions on Industrial Electronics, vol. 64, no. 3, pp. 2135–2146, 2017.CrossRefGoogle Scholar
  12. [12]
    N. Sun, Y. Fang, H. Chen, Y. Fu, and B. Lu, “Nonlinear stabilizing control for ship-mounted cranes with ship roll and heave movements: design, analysis, and experiments,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. PP, no. 99, pp. 1–13, 2017.Google Scholar
  13. [13]
    Q. Ruiyun, T. Gang, and X. Yao, “Adaptive control of discrete-time state-space T-S fuzzy systems with general relative degree,” Fuzzy Sets and Systems, vol. 217, pp. 22–40, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    C. Wu, J. Liu, H. Li, and L. Wu, “Adaptive fuzzy control for nonlinear networked control systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2420–2430, 2017.CrossRefGoogle Scholar
  15. [15]
    Z. Bouchama, N. Essounbouli, M. N. Harmas, and K. Saoudi, “Reaching phase free adaptive fuzzy synergetic power system stabilizer,” International Journal of Electrical Power & Energy Systems, vol. 77, pp. 43–49, 2016.CrossRefGoogle Scholar
  16. [16]
    D. Da-Wei, L. Xiaoli, Y. Wang, and Z. Shi, “Non-fragile H¥ fuzzy filtering for discrete-time nonlinear systems,” IET Control Theory & Applications, vol. 6, pp. 848–857, 2013.Google Scholar
  17. [17]
    Q. Ruiyun and A. B. Mietek, “Stable indirect adaptive control based on discrete-time T-S fuzzy model,” Fuzzy Sets and Systems, vol. 159, pp. 900–925, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    L. Haitao and Z. Tie, “Fuzzy sliding mode control of robotic manipulators with kinematic and dynamic uncertainties,” J. Dyn. Sys., Meas., Control, vol. 134, no. 6, 2008.Google Scholar
  19. [19]
    S. Larguech, S. Aloui, P. Olivier, A. El-Hajjaji, and A. Chaari, “Fuzzy sliding mode control for turbocharged diesel engine,” J. Dyn. Sys., Meas., Control, vol. 138, no. 1, 2015.Google Scholar
  20. [20]
    Q. Ruiyun, T. Gang, J. Bin, and T. Chang, “Adaptive control schemes for discrete-time T-S fuzzy systems with unknown parameters and actuator failures,” IEEE Transactions on Fuzzy Systems, vol. 20, pp. 471–486, 2012.CrossRefGoogle Scholar
  21. [21]
    A. Kolesnikov, G. Veselov, A. Kuzmenko, A. Popov, and A. Kuzmenko, Modern Applied Control Theory:Synergetic Approach in Control Theory, TSURE Press, Moscow-Taganrog, 2, 2000.Google Scholar
  22. [22]
    A. Kolesnikov, A. Monti, F. Ponci, E. Santi, and R. Dougal, “Synergetic synthesis of dc-dc boost converter controllers: Theory and experimental analysis,” Proc. Int. Conf. of IEEE Applied Power Electronics Conference, vol. 1, pp. 409–415, 2002.Google Scholar
  23. [23]
    Q. Wang, J. Feng, and T. Li, “Analysis of the synergetic control based on variable structure and application of power electronics,” Proc. Int.Conf. on Information Engineering and Computer Science, vol. 1, 2009.Google Scholar
  24. [24]
    L. X. Wang, “Stable adaptive fuzzy control of nonlinear systems,” IEEE Trans Fuzzy Sys, vol. 1, pp. 146–155, 1993.CrossRefGoogle Scholar
  25. [25]
    B. Kosko, “Fuzzy systems as universal approximators,” Proc. Int. Conf. IEEE Fuzzy Systems, vol. 1, pp. 1329–1333, 1992.zbMATHGoogle Scholar
  26. [26]
    M. B. Kadri, “Comparison of fuzzy identification schemes for robust control performance of an adaptive fuzzy controller,” Arabian Journal for Science and Engineering, vol. 39, no. 3, pp. 2013–2019, 2014.MathSciNetCrossRefGoogle Scholar
  27. [27]
    A. M. Zaki, M. El-Bardini, F. A. S. Soliman, and M. Sharaf, “Embedded indirect adaptive fuzzy controller based on T-S fuzzy inverse model,” Arabian Journal for Science and Engineering, vol. 7, no. 9, pp. 1–11, 2013.Google Scholar
  28. [28]
    L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice-Hall, 1994.Google Scholar
  29. [29]
    H. Sheng, W. Huang, T. Zhang, and X. Huang, “Robust adaptive fuzzy control of compressor surge using backstepping,” Arabian Journal for Science and Engineering, vol. 39, no. 12, pp. 9301–9308, 2014.CrossRefGoogle Scholar
  30. [30]
    Z. Xiao, T. Li, and Z. Li, “A novel single fuzzy approximation based adaptive control for a class of uncertain strictfeedback discrete-time nonlinear systems,” Neurocomputing, vol. 39, no. 167, pp. 179–186, 2015.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Boukhalfa Abdelouaheb
    • 1
    Email author
  • Khaber Farid
    • 1
  • Essounbouli Najib
    • 2
  1. 1.QUERE Laboratory, Department of Electrical EngineeringFerhat Abbas UniversitySétif1Algeria
  2. 2.CReSTIC LaboratoryUniversity of Reims Champagne ArdennePairsFrance

Personalised recommendations