Observer-based Composite Adaptive Dynamic Terminal Sliding-mode Controller for Nonlinear Uncertain SISO Systems

  • Xiaofei Liu
  • Shengbo QiEmail author
  • Reza Malekain
  • Zhixiong Li
Regular Papers Control Theory and Applications


In the present paper, the observer-based composite adaptive terminal sliding-mode control is investigated for the nonlinear uncertain system. First, an adaptive observer is designed to estimate the unavailable high-order derivative of the output. Then, a new dynamic terminal sliding surface is proposed with a state filter, which aims to develop the dynamic terminal sliding mode controller. By the composite adaptive control methods, a new adaptive law is designed, and the stability of the overall system is proofed based on the Lyapunov method. Finally, some numerical simulations are conducted to validate the effectiveness of the proposed algorithm.


Adaptive control adaptive observer dynamic terminal sliding mode control stability 


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  1. [1]
    Y. Wei, J. H. Park, and J. Qiu, “Sliding mode control for semi–Markovian jump systems via output feedback,” Automatica, vol. 81, pp. 133–141, April 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    W. Qi and G. Zong, “Observer–based adaptive SMC for nonlinear uncertain singular semi–Markov jump systems with applications to DC motor,” IET Control Theory and Applications, vol. 11, pp. 1504.1513, 2017.Google Scholar
  3. [3]
    K. Park and T. Tsuji, “Terminal sliding mode control of second–order nonlinear uncertain systems,” Int. J. Robust Nonlinear Control, vol. 9, pp. 769–780, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Y. Feng, X. Yu, and Z. Man, “Nonsingular terminal sliding mode control of rigid robot manipulators,” Automatica, vol. 38, pp. 2159.2167, 2002.Google Scholar
  5. [5]
    J. Liu and F. Sun, “A novel dynamic terminal sliding mode control of uncertain nonlinear systems,” Journal of Control Theory and Applications, vol. 5, no. 2, pp. 189–193, 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. Chen, Q. Wu, and R. Cui, “Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems,” ISA Transactions, vol. 52, pp. 198–206, 2013.CrossRefGoogle Scholar
  7. [7]
    J. Xiong and G. Zhang, “Global fast dynamic terminal sliding mode control for a quadrotor UAV,” ISA Transactions, vol. 66, pp. 233–240, 2017.CrossRefGoogle Scholar
  8. [8]
    M. Zak, “Terminal attractors for addressable memory in neural networks,” Physics Letter, vol. 133, no. 12, pp. 18–22, 1988.CrossRefGoogle Scholar
  9. [9]
    C. Yu, M. Xie, and J. Xie, “Sliding mode tracking control of nonlinear system with non–matched uncertainties,” Journal of Shanghai Jiaotong University, vol. 35, no. 8, pp. 1141–1143, 2001.zbMATHGoogle Scholar
  10. [10]
    S. Mobayen and F. Tchier, “A novel robust adaptive second–order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1197–1106, 2017.CrossRefGoogle Scholar
  11. [11]
    X. Ma, F. Sun, H. B. Li, and B. He, “Neural–networkbased integral sliding–mode tracking control of secondorder multi–agent systems with unmatched disturbances and completely unknown dynamics,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1925–1935, 2017.CrossRefGoogle Scholar
  12. [12]
    M. Chen, C. Chen, and F. Yang, “An LTR–observer based dynamic sliding mode control for chattering reduction,” Automatica, vol. 453, pp. 1111.1116, 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    J. Slotine and W. Li, Applied Nonlinear Control, Prentice–Hall, Englewood Cliffs, NJ, 1991.zbMATHGoogle Scholar
  14. [14]
    J. Nakanishi, J. Farrell, and S. Schaal, “Composite adaptive control with locally weighted statistical learning,” Neural Networks, vol. 18, pp. 71–90, 2005.CrossRefzbMATHGoogle Scholar
  15. [15]
    P. Ioannou and J. Sun, Robust Adaptive Control, Prentice Hall, Englewood Cliffs, NJ, 1996.zbMATHGoogle Scholar
  16. [16]
    Y. Leu, T. Lee, and W. Wang, “Observer–based adaptive fuzzy–neural control for unknown nonlinear dynamical systems,” IEEE Trans. Systems Man Cybernet. Part B: Cybernet, vol. 29, pp. 583–591, 1999.CrossRefGoogle Scholar
  17. [17]
    C. Kung and T. Chen, “Observer–based indirect adaptive fuzzy sliding mode control with state variable filter for unknown nonlinear dynamical systems,” Fuzzy Set and Systems, vol. 155, pp. 292–308, 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    A. Boulkroune, M. Tadjine, M. M’Saad, and M. Farza, “How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems,” Fuzzy Set and Systems, vol. 159, pp. 926–948, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    C. Hyun, C. Park, and S. Kim, “Takagi–Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design,” Information Sciences, vol. 180, pp. 2314.2327, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Y. Wang, T. Chai, and Y. Zhang, “State observer–based adaptive fuzzy output–feedback control for a class of uncertain nonlinear systems,” Information Sciences, vol. 180, pp. 5029.5040, 2010.Google Scholar
  21. [21]
    Y. Wei, J. H. Park, H. R. Karimi, and Y. C. Tian, “Improved stability and stabilization results for stochastic synchronization of continuous–time semi–Markovian jump,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 6, pp. 2488–2501, 2018.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Y. Wei, J. Qiu, and H. R. Karimi, “Fuzzy–affine–modelbased memory filter design of nonlinear systems with timevarying delay,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 504–517, 2018.CrossRefGoogle Scholar
  23. [23]
    M. Zeinali and L. Notash, “Adaptive sliding mode control with uncertainty estimator for robot manipulators,” Mechanism and Machine Theory, vol. 45, pp. 80–90, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    C. Veluvolu and D. Lee, “Sliding mode high–gain observers for a class of uncertain nonlinear systems,” Applied Mathematics Letters, vol. 24, pp. 329–334, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    H. Li, P. Shi, D. Yao, and L. Wu, “Observer–based adaptive sliding mode control for nonlinear Markovian jump systems,” Automatica, vol. 64, pp. 133–142, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    C. C. Hang, “On state variable filters for adaptive system design,” IEEE Trans. Automatic Control, vol. 21, no. 6, pp. 874–876, 1976.CrossRefzbMATHGoogle Scholar
  27. [27]
    E. Lavretsky, “Combined/composite model reference adaptive control,” IEEE Trans. Automatic Control, vol. 54, no. 11, pp. 2692–2697, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Y. Pan, Y. Zhou, T. Sun, and J. Meng, “Composite adaptive fuzzy H¥ tracking control of uncertain nonlinear systems,” Neurocomputing, vol. 99, pp. 15–24, 2013.CrossRefGoogle Scholar
  29. [29]
    P. Ioannou and P. Kokotovic, “Instability analysis and improvement of robustness of adaptive control,” Automatica, vol. 20, pp. 583–594, 1984.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    S. Blazic, D. Matko, and I. Skrjanc, “Adaptive law with a new leakage term,” IET Control Theory Appl., vol. 4, no. 9, pp. 1533–1542, 2010.MathSciNetCrossRefGoogle Scholar
  31. [31]
    H. Khalil, Nonlinear Systems, Prentice–Hall, Englewood Cliffs, NJ, 2002.zbMATHGoogle Scholar
  32. [32]
    H. Yong, L. Lewis, and T. Chaouki, “A dynamic recurrent neural–network–based adaptive observer for a class of nonlinear systems,” Automatica, vol. 33, pp. 1539.1543, 2003.Google Scholar
  33. [33]
    B. B. Letswamotse, R. Malekian, C. Y. Chen, K. M. Modieginyane, “Software defined wireless sensor networks (SDWSN): a review on efficient resources, applications and technologies,” Journal of Internet Technology, vol. 19, no. 5, pp. 1303–1313, 2018.Google Scholar
  34. [34]
    X. Jin, J. Shao, X. Zhang, W. An, and R. Malekian, “Modeling of nonlinear system based on deep learning framework,” Nonlinear Dynamics, vol. 84, no. 3, pp. 1327–1340, 2016.MathSciNetCrossRefGoogle 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 2019

Authors and Affiliations

  • Xiaofei Liu
    • 1
  • Shengbo Qi
    • 1
    Email author
  • Reza Malekain
    • 2
  • Zhixiong Li
    • 3
  1. 1.College of EngineeringOcean University of ChinaQingdaoChina
  2. 2.Department of Electrical, Electronic and Computer EngineeringUniversity of PretoriaPretoriaSouth Africa
  3. 3.School of Mechanical, Materials, Mechatronic and Biomedical EngineeringUniversity of WollongongWollongongAustralia

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