Nonlinear Dynamics

, Volume 88, Issue 4, pp 2553–2575 | Cite as

Observer-based fuzzy adaptive fault-tolerant nonlinear control for uncertain strict-feedback nonlinear systems with unknown control direction and its applications

  • Baraka Olivier Mushage
  • Jean Chamberlain Chedjou
  • Kyandoghere Kyamakya
Original Paper


This paper proposes a new nonlinear control scheme incorporating a state observer, a fuzzy neural network (FNN) and a new Nussbaum function for strict-feedback nonlinear systems by considering several challenges. These challenges are external disturbances, uncertain dynamics, unmeasured states, constrained input, unknown control direction, singularity issue, and actuator’s faults of different types. The scheme uses approximations of the unknown system’s dynamics provided by the FNN, the system’s states variables estimation provided by a model-free high-gain observer, and the control direction provided by the Nussbaum function. Compared to existing schemes, in addition to the fact that the new scheme can tackle simultaneously all the aforementioned challenges with better tracking performances, it also cancels the assumption about the positive definiteness of the control gain function found in many works. Thus, the scheme suites for more applications as it can be applied in cases where the control gain can be either semi-negative/negative-definite, semi-positive/positive-definite. Furthermore, the knowledge of the bounds for uncertain dynamics, actuation faults, FNN approximation errors and external disturbances is not required as it is for many other schemes. The effectiveness of the scheme is illustrated by its successful application to three examples, which are the pitch angle control for a Boeing 747-100/200 represented by the ultimate approximate nonlinear longitudinal model over up-and-away flight regime, the trajectory tracking control of a one-link manipulator actuated by a brush DC (BDC) motor, and the position tracking control for an inverted pendulum.


Strict-feedback Actuator fault Adaptive nonlinear control Nussbaum function Fuzzy neural network High-gain state observer 


  1. 1.
    Hu, Q., Xiao, B.: Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of effectiveness. Nonlinear Dyn. 64, 13–23 (2011)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Choi, H.H., Jung, J.-W.: Fuzzy speed control with an acceleration observer for a permanent magnet synchronous motor. Nonlinear Dyn. 67, 1717–1727 (2012)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Gao, G., Wang, J.: Observer-based fault-tolerant control for an air-breathing hypersonic vehicle model. Nonlinear Dyn. 76, 409–430 (2014)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Zhao, B., Li, Y.: Local joint information based active fault tolerant control for reconfigurable manipulator. Nonlinear Dyn. 77, 859–876 (2014)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Yue, M., Liu, B., An, C., Sun, X.: Extended state observer-based adaptive hierarchical sliding mode control for longitudinal movement of a spherical robot. Nonlinear Dyn. 78, 1233–1244 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Xu, Y., Tong, S., Li, Y.: Prescribed performances fuzzy adaptive fault-tolerant control of nonlinear systems with actuator faults. IET Control Theory Appl. 6, 420–431 (2014)CrossRefGoogle Scholar
  7. 7.
    Chang, W., Park, J.B., Joo, Y.H., Chen, G.: Design of robust fuzzy-model-based controller with sliding mode control for SISO nonlinear systems. Fuzzy Sets Syst. 125, 1–22 (2002)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Li, Y., Tong, S., Li, T.: Adaptive fuzzy output-feedback control for output constrained nonlinear systems in the presence of input saturation. Fuzzy Sets Syst. 248, 138–155 (2015)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Li, Y.-X., Yang, G.-H.: Robust fuzzy adaptive fault-tolerant control for a class of nonlinear systems with mismatched uncertainties and actuator faults. Nonlinear Dyn. 81, 395–409 (2015)CrossRefMATHGoogle Scholar
  10. 10.
    Ho, H.F., Wong, Y.K., Rad, A.B., Lo, W.L.: State observer based indirect adaptive fuzzy tracking control. Simul. Model Pract. Theory 13, 646–663 (2015)CrossRefGoogle Scholar
  11. 11.
    Boulkroune, A., Tadjine, M., M’Saad, M., Farza, M.: Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction. Fuzzy Sets Syst. 161, 797–820 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Boulkroune, A.: A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign. Neurocomputing 179, 318–325 (2016)CrossRefGoogle Scholar
  13. 13.
    Zhang, T., Shi, X., Zhu, Q., Yang, Y.: Adaptive neural tracking of pure-feedback nonlinear systems with unknown gain signs and unmodeled dynamics. Neurocomputing 121, 290–297 (2013)CrossRefGoogle Scholar
  14. 14.
    Mushage, B.O., Chedjou, J.C., Kyamakya, K.: An extended Neuro-Fuzzy-based robust adaptive sliding mode controller for linearizable systems and its applications on a new chaotic system. Nonlinear Dyn. 83, 1601–1619 (2016)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Wang, T., Xie, W., Zhang, Y.: Sliding mode fault tolerant control dealing with modeling uncertainties and actuator faults. ISA Trans. 51, 386–392 (2012)CrossRefGoogle Scholar
  16. 16.
    Cui, Y., Zhang, H., Wang, Y., Gao, W.: Adaptive control for a class of uncertain strict-feedback nonlinear systems based on a generalized fuzzy hyperbolic model. Fuzzy Sets Syst. 302, 52 (2016). doi: 10.1016/j.fss.2015.11.015 MathSciNetCrossRefGoogle Scholar
  17. 17.
    Carroll, J., Dawson, D.: Integrator backstepping techniques for the tracking control of permanent magnet brush DC motors. IEEE Trans. Ind. Appl. 31, 248–255 (1995)CrossRefGoogle Scholar
  18. 18.
    Isidori, A.: Nonlinear Control Syst. Introd. Springer-Verlag, New-York (1995)CrossRefGoogle Scholar
  19. 19.
    Shen, Q., Jiang, B., Shi, P., Lim, C.C.: Novel neural networks-based fault tolerant control scheme with fault alarm. IEEE Tract. Cybern. 44, 2190–2201 (2014)CrossRefGoogle Scholar
  20. 20.
    Wu, J., Chen, W., Li, J.: Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy. Fuzzy Sets Syst. 273, 1–25 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Li, I.-H., Lee, L.-W., Chiang, H.-H., Chen, P.-C.: Intelligent switching adaptive control for uncertain nonlinear dynamical systems. Appl. Soft Comput. 34, 638–654 (2015)CrossRefGoogle Scholar
  22. 22.
    Shen, Q., Jiang, B., Cocquempot, V.: Fault tolerant control for T-S fuzzy systems with applications to near space hypersonic vehicle with actuator faults. IEEE Trans. Fuzzy Syst. 20, 652–665 (2012)CrossRefGoogle Scholar
  23. 23.
    Shen, Q., Jiang, B., Cocquempot, V.: Fuzzy logic system-based adaptive fault tolerant control for near space vehicle attitude dynamics with actuator faults. IEEE Trans. Fuzzy Syst. 21, 289–300 (2013)CrossRefGoogle Scholar
  24. 24.
    Zhang, Y.M., Jiang, J.: Fault tolerant control system design with explicit consideration of performance degradation. IEEE Trans. Aerosp. Electron. Syst. 39, 838–848 (2003)CrossRefGoogle Scholar
  25. 25.
    Hu, Q., Shi, P., Gao, H.: Adaptive variable structure and commanding shaped vibration control of flexible spacecraft. J Guid. Control Dyn. 30, 804–815 (2007)CrossRefGoogle Scholar
  26. 26.
    Shen, Q., Wang, D., Zhu, S., Poh, E.K.: Integral-type sliding mode fault-tolerant control for attitude stabilization of spacecraft. IEEE Trans. Control Syst. Technol. 23, 1131–1138 (2015)CrossRefGoogle Scholar
  27. 27.
    Jin, J., Ko, S., Ryoo, C.K.: Fault tolerant control for satellites with four reaction wheels. Control Eng. Pract. 16, 1250–1258 (2008)CrossRefGoogle Scholar
  28. 28.
    Xia, B., Hu, Q.L., Zhang, Y.M.: Fault-tolerant attitude control for flexible spacecraft without angular velocity magnitude measurement. J. Guid. Control Dyn. 34, 1556–1561 (2011)CrossRefGoogle Scholar
  29. 29.
    Benosman, M., Lum, K.-Y.: Application of absolute stability theory to robust control against loss of actuator effectiveness. IET Control Theory Appl. 3, 772–788 (2009)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Shi, W.: Observer-based indirect adaptive fuzzy control for SISO nonlinear systems with unknown gain sign. Neurocomputing 171, 1598–1605 (2016)CrossRefGoogle Scholar
  31. 31.
    Liu, Y.-J., Tong, S.-C., Wang, W., Li, Y.-M.: Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications. Int. J. Control Autom. Syst. 7, 681–690 (2009)CrossRefGoogle Scholar
  32. 32.
    Goléa, N., Goléa, A., Barra, K., Bouktir, T.: Observer-based adaptive control of robot manipulators: fuzzy systems approach. Appl. Soft Comput. 8, 778–787 (2008)CrossRefGoogle Scholar
  33. 33.
    Tong, S., Wang, T., Li, Y.: Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans. Fuzzy Syst. 22, 563–574 (2014)CrossRefGoogle Scholar
  34. 34.
    Márton, L.: Actuator fault diagnosis in mechanical systems-fault power estimation approach. Int. J. Control Autom. Syst. 13, 110–119 (2015)CrossRefGoogle Scholar
  35. 35.
    Brambilla, D., Capisani, L.M., Ferrara, A., Pisu, P.: Fault detection for robot manipulators via second-order sliding modes. IEEE Trans. Ind. Electron. 55, 3954–3963 (2008)CrossRefGoogle Scholar
  36. 36.
    Tong, S., Li, H.-X.: High-gain observer with sliding mode for nonlinear state estimation and fault reconstruction. J. Frankl. Inst. 351, 1995–2014 (2014)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Veluvolu, K.C., Kim, M.Y., Lee, D.: Nonlinear sliding mode high-gain observers for fault estimation. Int. J. Syst. Sci. 42, 1065–1074 (2011)MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Gholami, A., Markazi, A.H.D.: A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems. Nonlinear Dyn. 70, 2095–2105 (2012)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Tong, S., Li, H.-X.: Fuzzy adaptive sliding-Mode control for MIMO nonlinear Systems. IEEE Trans. Fuzzy Syst. 11, 354–360 (2003)CrossRefGoogle Scholar
  40. 40.
    Ye, X.: Adaptive nonlinear output-feedback control with unknown high-frequency gain sign. IEEE Trans. Autom. Control 46(1), 112–115 (2001)MathSciNetCrossRefMATHGoogle Scholar
  41. 41.
    Lozano, R., Moctezuma, R.G.: Model reference adaptive control with unknown high frequency gain sign. Automatica 29(6), 1565–1569 (1993)MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Xu, Y., Tong, S., Li, Y.: Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults based on dynamic surface. J. Frankl. Instit. 350, 1768–1786 (2013)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Hao, L.-Y., Park, J.H., Ye, D.: Fuzzy logic systems-based integral sliding mode fault-tolerant control for a class of uncertain non-linear systems. IET Control Theory Appl. 10, 300–311 (2016)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Hao, L.-Y., Park, J.H., Ye, D.: Integral sliding mode fault-tolerant control for uncertain linear systems over networks with signals quantization. IEEE Transactions on Neural Networks and Learning Systems (2016). doi: 10.1109/TNNLS.2016.2574905 Google Scholar
  45. 45.
    Hao, L.-Y., Yang, G.-H.: Robust adaptive fault-tolerant control of uncertain linear systems via sliding-mode output feedback. Int. J. Robust Nonlinear Control 25, 2461–2480 (2015)MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    Niemann, H., Stroustrup, J.: Passive fault tolerant control of a double inverted pendulum-a case study. Control Eng. Practice 13, 1047–1059 (2004)CrossRefGoogle Scholar
  47. 47.
    Pan, Y., Liu, Y., Yu, H.: Simplified adaptive neural control of strict-feedback nonlinear systems. Neurocomputing 159, 251–256 (2015)CrossRefGoogle Scholar
  48. 48.
    Shen, H., Park, J.H., Wu, Z.-G.: Finite-time reliable \(L_2\)-\(L_{\infty }/H_{\infty }\) control for Takagi-Sugeno fuzzy systems with actuator faults. IET Control Theory Appl. 8, 688–696 (2014)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Shen, H., Wu, Z.-G., Park, J.H.: Reliable mixed passive and \(H_{\infty }\) filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures. Int. J. Robust Nonlinear Control 25, 3231–3251 (2015)Google Scholar
  50. 50.
    Pratap, B., Purwar, S.: Sliding mode state observer for 2-DOF twin rotor MIMO system. In: 2010 International Conference on Power. Control and Embedded Systems (ICPCES), pp. 1–6. IEEE, Allahabad (2010)Google Scholar
  51. 51.
    Veluvolu, K.C., Zhe, F., Soh, Y.C.: Nonlinear sliding mode high-gain observers for fault detection. In: 2010 International Workshop on Variable Structure Systems, pp. 206–208. IEEE, Mexico City (2010)Google Scholar
  52. 52.
    Veluvolu, K.C., Soh, Y.C., Cao, W.: Robust observer with sliding mode estimation for nonlinear uncertain systems. IET Control Theory Appl. 1(5), 1533–1540 (2007)MathSciNetCrossRefMATHGoogle Scholar
  53. 53.
    Skogestad, S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 13, 291–309 (2003)CrossRefGoogle Scholar
  54. 54.
    Chakravarty, A., Mahanta, C.: Actuator fault tolerant control scheme for nonlinear uncertain systems using backstepping based sliding mode. In: Proceedings of the 2013 Annual IEEE India Conference (INDICON), pp. 1–6. IEEE, Mumbai (2013)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Baraka Olivier Mushage
    • 1
  • Jean Chamberlain Chedjou
    • 1
  • Kyandoghere Kyamakya
    • 1
  1. 1.Institute of Smart Systems TechnologiesAlpen-Adria-Universität KlagenfurtKlagenfurtAustria

Personalised recommendations