Disturbance Observer-based Adaptive Fault-tolerant Dynamic Surface Control of Nonlinear System with Asymmetric Input Saturation

  • Li WangEmail author
  • Hua-Jun Gong
  • Chun-Sheng Liu


In this paper, a composite fault-tolerant control problem is studied for a class of uncertain nonlinear system with asymmetric input constraint, actuator fault and external unmatched disturbance. The radial basis function neural network (RBFNN) is employed to approximate the unknown uncertainty and asymmetric input saturation. The approximation error, external unmatched disturbance and actuator faults are integrated as the compounded disturbance. A nonlinear disturbance observer is designed to tackle the effect of the compounded disturbance which can be separated from the controller design. To handle the effect of asymmetric input saturation, a smooth continuous differentiable saturation model is explored. Adaptive NN fault-tolerant control scheme is developed to guarantee that all the signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) and the tracking errors converge to a small neighborhood of origin by choosing the appropriate design parameters. The effectiveness of the proposed control scheme is demonstrated in the simulation study.


Disturbance observer fault-tolerant input saturation nonlinear system robust control 


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  1. [1]
    J. Rubio, “Robust feedback linearization for nonlinear processes control,” ISA Transactions, vol. 74, pp. 155–164, March 2018.CrossRefGoogle Scholar
  2. [2]
    J. Meda, “Estimation of complex systems with parametric uncertainties using a jssf heuristically adjusted,” IEEE Latin America Transactions, vol. 16, no. 2, pp. 350–357, Feburary 2018.CrossRefGoogle Scholar
  3. [3]
    J. Rubio, J. Lopez, J. Pacheco, and R. Encinas, “Control of two electrical plants,” Asian Journal of Control, vol. 20, no. 4, pp. 1504–1518, July 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Rubio, J. Pieper, and G. Gutierrez, “Modeling and regulation of two mechanical systems,” IET Science, Measurement & Technology, vol. 12, no. 5, pp. 657–665, January 2018.CrossRefGoogle Scholar
  5. [5]
    M. Chen, G. Tao, and B. Jiang, “Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 9, pp. 2086–2097, September 2015.MathSciNetCrossRefGoogle Scholar
  6. [6]
    S. Gao, H. Dong, B. Ning, and L. Chen, “Neural adaptive control for uncertain nonlinear system with input saturation: state transformation based output feedback,” Neurocomputing, vol. 159, pp. 117–125, July 2015.CrossRefGoogle Scholar
  7. [7]
    Q. Zhou, L. Wang, C. Wu, H. Li, and H. Du, “Adaptive fuzzy control for nonstrict–feedback systems with input saturation and output constraint,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 47, no. 1, pp. 1–12, January 2017.CrossRefGoogle Scholar
  8. [8]
    J. Ma, S. Ge, Z. Zheng, and D. Hu, “Adaptive NN control of a class of nonlinear systems with asymmetric saturation actuators,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 7, pp. 1532–1538, July 2015.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Z. Chen, Z. Li, and C. Chen, “Adaptive neural control of uncertain MIMO nonlinear systems with state and input constraints,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no.6, pp. 1318–1330, June 2017.Google Scholar
  10. [10]
    W. Si and X. Dong, “Adaptive neural control for MIMO stochastic nonlinear pure–feedback systems with input saturation and full–state constraints,” Neurocomputing, vol. 275, pp. 298–307, 2018.CrossRefGoogle Scholar
  11. [11]
    K. Yong, M. Chen, and Q. Wu, “Constrained adaptive neural control for a class of nonstrict–feedback nonlinear systems with disturbances,” Neurocomputing, vol. 272, pp. 405–415, July 2018.CrossRefGoogle Scholar
  12. [12]
    A. Shafiekhani, J. Mahjoob, and M. Akraminia, “Design and implementation of an adaptive critic–based neurofuzzy controller on an unmanned bicycle,” Mechatronics, vol. 28, pp. 115–123, 2015.CrossRefGoogle Scholar
  13. [13]
    J. Kim and N. Kasabov, “HyFIS: adaptive neuro–fuzzy inference systems and their application to nonlinear dynamical systems,” Neural Networks, vol.12, no. 9, pp. 1301–1319, November 1999.CrossRefGoogle Scholar
  14. [14]
    Y. Cui, H. Zhang, and Y. Wang, “Adaptive tracking control of uncertain MIMO nonlinear systems based on generalized fuzzy hyperbolic model,” Fuzzy Sets and Systems, vol. 306, pp. 105–117, January 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    S. Li, Y. Wang, and J. Tan, “Adaptive and robust control of quadrotor aircrafts with input saturation,” Nonlinear Dynamics, vol. 89. no. 1–2, pp.1–11, July 2017.Google Scholar
  16. [16]
    S. Gao, B. Ning, and H. Dong, “Fuzzy dynamic surface control for uncertain nonlinear systems under input saturation via truncated adaptation approach,” Fuzzy Sets and Systems, vol. 290, pp. 100–117, May 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    X. Wang, C. Tan, and D. Zhou, “A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions,” Automatica, vol. 79, pp. 290–295, May 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    J. Li and G. Yang, “Adaptive actuator failure accommodation for linear systems with parameter uncertainties,” IET Control Theory & Applications, vol. 6, no. 2, pp. 274–285, January 2012.MathSciNetCrossRefGoogle Scholar
  19. [19]
    C. Liu, B. Jiang, X. Song, and S. Zhang, “Fault–tolerant control allocation for over–actuated discrete–time systems,” Journal of the Franklin Institute, vol. 352, no. 6, pp. 2297–2313, June 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    M. Khalili, X. Zhang, M. Polycarpou, T. Parisini, and Y. Cao, “Distributed adaptive fault–tolerant control of uncertain multi–agent systems,” IFAC–PapersOnLine, vol. 48, no. 21, pp. 142–151, 2018.MathSciNetzbMATHGoogle Scholar
  21. [21]
    C. Wang, C. Wen, and L. Guo, “Decentralized outputfeedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures,” Automatica, vol. 71, pp. 187–196, September 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    Y. Li, T. Li, and X. Jing, “Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function,” International Journal of Adaptive Control and Signal Processing, vol. 28. no. 2, 184–199, February 2014.Google Scholar
  23. [23]
    M. Chen and B. Jiang, “Robust bounded control for uncertain flight dynamics using disturbance observer,” Journal of Systems Engineering and Electronics, vol. 25, no. 4, pp. 640–647, 2014.CrossRefGoogle Scholar
  24. [24]
    B. Ren, S. Ge, K. Tee, and T. Lee, “Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1339–1345, July 2010.CrossRefGoogle Scholar
  25. [25]
    Y. Cui, H. Zhang, Q. Qu, and C. Luo, “Synthetic adaptive fuzzy tracking control for MIMO uncertain nonlinear systems with disturbance observer,” Neurocomputing, vol. 249, pp. 191–201, August 2017.CrossRefGoogle Scholar
  26. [26]
    M. Lv, Y. Wang, S. Baldi, Z. Liu, and Z. Wang, “A Dsc method for strict–feedback nonlinear systems with possibly unbounded control gain functions,” Neurocomputing, vol. 275, pp. 1383–1392, 2018.CrossRefGoogle Scholar
  27. [27]
    D. Wang and J. Huang, “Neural network–based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict–feedback form,” IEEE Transactions on Neural Networks, vol. 28, no. 9, pp. 2156–2167, Janurary 2017.MathSciNetGoogle Scholar
  28. [28]
    S. Gao, H. Dong, B. Ning, and X. Yao, “Single–parameterlearning–based fuzzy fault–tolerant output feedback dynamic surface control of constrained–input nonlinear systems,” Information Sciences, vol. 385, pp. 378–394, April 2017.CrossRefGoogle Scholar
  29. [29]
    H. Wang, B. Chen, C. Lin, and Y. Sun, “Observer–based neural adaptive control for a class of MIMO delayed nonlinear systems with input nonlinearities,” Neurocomputing, vol. 275, pp. 1988–1997, 2018.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 2019

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsJiangsu NanjingChina
  2. 2.Nanhang Jincheng CollegeJiangsu NanjingChina

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