International Journal of Fuzzy Systems

, Volume 21, Issue 3, pp 755–768 | Cite as

Adaptive Fuzzy Sliding Mode Control for Nonlinear Uncertain SISO System Optimized by Differential Evolution Algorithm

  • Cao Van Kien
  • Nguyen Ngoc Son
  • Ho Pham Huy AnhEmail author


In this paper, a new adaptive fuzzy sliding mode controller (AFSMC) is proposed for single-input single-output (SISO) nonlinear systems with uncertainties and external disturbances. An adaptive fuzzy model is used to approximate the unknown and uncertain features of a nonlinear system. Furthermore, the fuzzy model parameters are optimally identified with a differential evolution algorithm. The novel AFSMC algorithm is designed using sliding mode control. The adaptive fuzzy law is adaptively generated with constraints based on Lyapunov stability theory to guarantee the asymptotic stability of the closed-loop nonlinear uncertain SISO system. Experimental results are presented to demonstrate that the proposed AFSMC provides a robust and simple approach to effectively control the highly nonlinear uncertain SISO systems.


Adaptive fuzzy sliding mode control (AFSMC) Differential evolution (DE) algorithm Pneumatic artificial muscle (PAM) Nonlinear uncertain SISO systems Fuzzy logic 



This research is funded by Ho Chi Minh City University of Technology-VNU-HCM under grant number TNCS-ĐĐT-2017-04 and by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number C2018-20-07.


  1. 1.
    Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-Mechanical Systems. CRC Press, Boca Raton (2009)CrossRefGoogle Scholar
  2. 2.
    Young, K.D., Utkin, V.I., Ozguner, U.: A control engineer’s guide to sliding mode control. IEEE Trans. Control Syst. Technol. 7(3), 328–342 (1999)CrossRefGoogle Scholar
  3. 3.
    Shtessel, Y., et al.: Sliding Mode Control and Observation, vol. 10. Birkhäuser, New York (2014)CrossRefGoogle Scholar
  4. 4.
    Wang, W.-Y., et al.: H/sub/spl infin//tracking-based sliding mode control for uncertain nonlinear systems via an adaptive fuzzy–neural approach. IEEE Trans. Syst. Man Cybern. B Cybern. 32(4), 483–492 (2002)CrossRefGoogle Scholar
  5. 5.
    Li, H., Wang, J., Shi, P.: Output-feedback based sliding mode control for fuzzy systems with actuator saturation. IEEE Trans. Fuzzy Syst. 24(6), 1282–1293 (2016)CrossRefGoogle Scholar
  6. 6.
    Nekoukar, V., Erfanian, A.: Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems. Fuzzy Sets Syst. 179(1), 34–49 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Yang, Y., Yan, Y.: Neural network approximation-based nonsingular terminal sliding mode control for trajectory tracking of robotic airships. Aerosp. Sci. Technol. 54, 192–197 (2016)CrossRefGoogle Scholar
  8. 8.
    Ma, X., et al.: Neural-network-based sliding-mode control for multiple rigid-body attitude tracking with inertial information completely unknown. Inf. Sci. 400, 91–104 (2017)CrossRefGoogle Scholar
  9. 9.
    Zou, A.-M., et al.: Finite-time attitude tracking control for spacecraft using terminal sliding mode and Chebyshev neural network. IEEE Trans. Syst. Man Cybern. B Cybern. 41(4), 950–963 (2011)CrossRefGoogle Scholar
  10. 10.
    Wang, L., Chai, T., Zhai, L.: Neural-network-based terminal sliding-mode control of robotic manipulators including actuator dynamics. IEEE Trans. Industr. Electron. 56(9), 3296–3304 (2009)CrossRefGoogle Scholar
  11. 11.
    Baek, J., Jin, M., Han, S.: A new adaptive sliding-mode control scheme for application to robot manipulators. IEEE Trans. Ind. Electron. 63(6), 3628–3637 (2016)CrossRefGoogle Scholar
  12. 12.
    Moussaoui, S., Boulkroune, A.: Stable adaptive fuzzy sliding-mode controller for a class of underactuated dynamic systems. In: Chadli, M., Bououden, S., Zelinka, I. (eds.) Recent Advances in Electrical Engineering and Control Applications, pp. 114–124. Springer, Cham (2017)CrossRefGoogle Scholar
  13. 13.
    Khazaee, M., et al.: Adaptive fuzzy sliding mode control of input-delayed uncertain nonlinear systems through output-feedback. Nonlinear Dyn. 87(3), 1943–1956 (2017)CrossRefzbMATHGoogle Scholar
  14. 14.
    Lin, D., Wang, X.: Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation. Fuzzy Sets Syst. 161(15), 2066–2080 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Park, B.S., et al.: Adaptive neural sliding mode control of nonholonomic wheeled mobile robots with model uncertainty. IEEE Trans. Control Syst. Technol. 17(1), 207–214 (2009)CrossRefGoogle Scholar
  16. 16.
    Ho, H.F., Wong, Y.K., Rad, A.B.: Adaptive fuzzy sliding mode control design: Lyapunov approach. In: 5th Asian Control Conference, vol. 3. IEEE (2004)Google Scholar
  17. 17.
    Khanesar, M.A., et al.: Adaptive indirect fuzzy sliding mode controller for networked control systems subject to time-varying network-induced time delay. IEEE Trans. Fuzzy Syst. 23(1), 205–214 (2015)CrossRefGoogle Scholar
  18. 18.
    Guo, Y., Woo, P.-Y.: An adaptive fuzzy sliding mode controller for robotic manipulators. IEEE Trans. Syst. Man Cybern. A Syst. Hum. 33(2), 149–159 (2003)CrossRefGoogle Scholar
  19. 19.
    Rastegar, S., Araújo, R., Mendes, J.: Online identification of Takagi–Sugeno fuzzy models based on self-adaptive hierarchical particle swarm optimization algorithm. Appl. Math. Model. 45, 606–620 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Li, C., Zou, W., Zhang, N., Lai, X.: An evolving T–S fuzzy model identification approach based on a special membership function and its application on pump-turbine governing system. Eng. Appl. Artif. Intell. 69, 93–103 (2018)CrossRefGoogle Scholar
  21. 21.
    Dziwiński, P., Bartczuk, Ł., Tingwen, H.: A method for non-linear modelling based on the capabilities of PSO and GA algorithms. In: International Conference on Artificial Intelligence and Soft Computing, pp. 221–232, June 2017Google Scholar
  22. 22.
    Karaboga, D., Kaya, E.: Adaptive network based fuzzy inference system (ANFIS) training approaches: a comprehensive survey. Artif. Intell. Rev. (2018). Google Scholar
  23. 23.
    Son, N.N., Anh, H.P.H., Chau, T.D.: Adaptive neural model optimized by modified differential evolution for identifying 5-DOF robot manipulator dynamic system. Soft. Comput. 22(3), 979–988 (2018)CrossRefGoogle Scholar
  24. 24.
    Van Kien, C., Anh, H.P.H., Nam, N.T.: Cascade training multilayer fuzzy model for nonlinear uncertain system identification optimized by differential evolution algorithm. Int. J. Fuzzy Syst. 20(5), 1671–1684 (2018). CrossRefGoogle Scholar
  25. 25.
    Van Kien, C., Son, N. N., Anh, H.P.H.: Identification of 2-DOF pneumatic artificial muscle system with multilayer fuzzy logic and differential evolution algorithm. In: The 12th IEEE Conference on Industrial Electronics and Applications (ICIEA 2017), pp. 1261–1266 (2017)Google Scholar
  26. 26.
    Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Cao Van Kien
    • 1
  • Nguyen Ngoc Son
    • 2
  • Ho Pham Huy Anh
    • 1
    Email author
  1. 1.FEEEHo Chi Minh City University of Technology, VNU-HCMHo Chi Minh CityVietnam
  2. 2.Faculty of Electronics TechnologyIndustrial University of Ho Chi Minh CityHo Chi Minh CityVietnam

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