Skip to main content
SpringerLink
Log in

Observer-Based Adaptive Fuzzy Fault-Tolerant Control for Nonlinear Systems Using Small-Gain Approach

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper addresses the adaptive fault-tolerant control problem for a class of nonlinear systems with unmodeled dynamics, actuator faults and immeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions. A new input-driven filter is designed to cope with the problem caused by the immeasurable states, and the lower bound of the unknown function \(\vartheta _j({\bar{x}}_j)\) is contained in the filter. Based on backstepping technique, a recursive design process is designed for the considered nonlinear system. Combining input-to-state practically stable theory with small-gain approach, the designed adaptive fuzzy controller guarantees the semi-global uniform ultimate boundedness of all variables in the closed-loop system. The main contributions of this paper lie in that not only the nonlinear system under consideration is more general, but also an effective output-feedback control scheme is proposed for the investigated nonlinear system. Finally, simulation results are depicted to validate the efficiency of our presented control method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Pan, Y.P., Yu, H.Y.: Composite learning from adaptive dynamic surface control. IEEE Trans. Autom. Control 61(9), 2603–2609 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  2. Liu, H., Pan, Y.P., Li, S.G., Chen, Y.: Adaptive fuzzy backstepping control of fractional-order nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 2209–2217 (2017)

    Article  Google Scholar 

  3. Qiu, J.B., Ding, S.X., Gao, H.J., Yin, S.: Fuzzy-model-based reliable static output feedback \(H_{\infty }\) control of nonlinear hyperbolic PDE systems. IEEE Trans. Fuzzy Syst. 24(2), 388–400 (2016)

    Article  Google Scholar 

  4. Zhang, W.H., Su, H.: Fuzzy adaptive control of nonlinear MIMO systems with unknown dead zone outputs. J. Frankl. Inst. 355(13), 5690–5720 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  5. Su, H., Zhang, T.L., Zhang, W.H.: Fuzzy adaptive control for SISO nonlinear uncertain systems based on backstepping and small-gain approach. Neurocomputing 238(17), 212–226 (2017)

    Article  Google Scholar 

  6. Li, H.Y., Pan, Y.N., Zhou, Q.: Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2015)

    Article  Google Scholar 

  7. Su, X.J., Wu, L.G., Shi, P., Chen, C.L.P.: Model approximation for fuzzy switched systems with stochastic perturbation. IEEE Trans. Fuzzy Syst. 23(5), 1458–1473 (2015)

    Article  Google Scholar 

  8. Ahn, K.K., Nam, D.N.C., Jin, M.L.: Adaptive backstepping control of an electrohydraulic actuator. IEEE/ASME Trans. Mech. 19(3), 987–995 (2014)

    Article  Google Scholar 

  9. Li, Y.M., Tong, S.C., Li, T.S.: Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans. Cybern. 45(1), 138–149 (2015)

    Article  Google Scholar 

  10. Liu, Y.J., Tong, S.C., Chen, C.L.P., Li, D.J.: Neural controller design-based adaptive control for nonlinear MIMO systems with unknown hysteresis inputs. IEEE Trans. Cybern. 46(1), 9–19 (2016)

    Article  Google Scholar 

  11. Zhai, D., An, L.W., Li, J.H., Zhang, Q.L.: Adaptive fuzzy fault-tolerant control with guaranteed tracking performance for nonlinear strict-feedback systems. Fuzzy Sets Syst. 302(1), 82–100 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, H.Y., Shi, P., Yao, D.Y.: Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults. IEEE Trans. Autom. Control 62(4), 1933–1939 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Huo, B.Y., Tong, S.C., Li, Y.M.: Adaptive fuzzy fault-tolerant output feedback control for uncertain nonlinear systems with actuator faults. Int. J. Syst. Sci. 44(12), 2365–2376 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, X., Zhai, D., Dong, J.X., Zhang, Q.L.: Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems. J. Frankl. Inst. 355(1), 273–290 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu, Y.Y., Tong, S.C., Li, Y.M.: Prescribed performance fuzzy adaptive fault-tolerant control of non-linear systems with actuator faults. IET Control Theory Appl. 8(6), 420–431 (2014)

    Article  MathSciNet  Google Scholar 

  16. Chen, M., Tao, G.: Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone. IEEE Trans. Cybern. 46(8), 1851–1862 (2016)

    Article  Google Scholar 

  17. Liu, M., Ho, D.W.C., Shi, P.: Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance. Automatica 58, 5–14 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, Y.X., Yang, G.H.: Fuzzy adaptive output feedback fault-tolerant tracking control of a class of uncertain nonlinear systems with non-affine nonlinear faults. IEEE Trans. Fuzzy Syst. 24(1), 223–234 (2016)

    Article  Google Scholar 

  19. Xu, J.: Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems. Int. J. Robust Nonlinear Control 26(2), 286–302 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Chen, M., Shi, P., Lim, C.C.: Adaptive neural fault-tolerant control of a 3-DOF model helicopter system. IEEE Trans. Syst. Man Cybern. Syst. 46(2), 260–270 (2016)

    Article  Google Scholar 

  21. Yu, X., Li, P., Zhang, Y.M.: The design of fixed-time observer and finite-time fault-tolerant control for hypersonic gliding vehicles. IEEE Trans. Ind. Electron. 65(6), 4135–4144 (2018)

    Article  Google Scholar 

  22. Shen, Q.K., 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(2), 289–300 (2013)

    Article  Google Scholar 

  23. Xu, B., Guo, Y.Y., Yuan, Y., Fan, Y.H., Wang, D.W.: Fault-tolerant control using command-filtered adaptive back-stepping technique: application to hypersonic longitudinal flight dynamics. Int. J. Adapt. Control Signal Process. 30(4), 553–577 (2016)

    Article  MathSciNet  Google Scholar 

  24. Wang, F., Liu, Z., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone and dynamic uncertainties. Nonlinear Dyn. 79(3), 1693–1709 (2015)

    Article  MATH  Google Scholar 

  25. Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive quantized controller design via backstepping and stochastic small-gain approach. IEEE Trans. Fuzzy Syst. 24(2), 330–343 (2016)

    Article  Google Scholar 

  26. Zhou, Q., Li, H.Y., Wu, C.W., Wang, L.J., Ahn, C.K.: Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 1979–1989 (2017)

    Article  Google Scholar 

  27. Liu, Y.J., Tong, S.C.: Barrier lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica 76, 143–152 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  28. Yin, S., Gao, H.J., Qiu, J.B., Kaynak, O.: Adaptive fault-tolerant control for nonlinear system with unknown control directions based on fuzzy approximation. IEEE Trans. Syst. Man Cybern. Syst 47(8), 1909–1918 (2017)

    Article  Google Scholar 

  29. Li, H.Y., Bai, L., Zhou, Q., Lu, R.Q., Wang, L.J.: Adaptive fuzzy control of stochastic nonstrict-feedback nonlinear systems with input saturation. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 2185–2197 (2017)

    Article  Google Scholar 

  30. Yang, H.Y., Wang, H.Q.: Robust adaptive fault-tolerant control for uncertain nonlinear system with unmodeled dynamics based on fuzzy approximation. Neurocomputing 173(3), 1660–1670 (2016)

    Article  Google Scholar 

  31. Jiang, Z.P.: A combined backstepping and small-gain approach to adaptive output feedback control. Automatica 35(6), 1131–1139 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang, L.X., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)

    Article  Google Scholar 

  33. Su, H., Zhang, W.H.: Adaptive fuzzy FTC design of nonlinear stochastic systems with actuator faults and unmodeled dynamics. Int. J. Adapt. Control Signal Process. 32(7), 1081–1101 (2018)

    Article  MATH  Google Scholar 

  34. Xue, L.R., Zhang, W.H., Lin, Y.N.: Global output tracking control for high-order stochastic nonlinear systems with SISS inverse dynamics and time-varying delays. J. Frankl. Inst. 353(13), 3249–3270 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61573227, 61633014, 61703248), the Research Fund for the Taishan Scholar Project of Shandong Province of China and SDUST Research Fund (No. 2015TDJH105).

Author information

Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Hang Su & Weihai Zhang

Authors
  1. Hang Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weihai Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weihai Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, H., Zhang, W. Observer-Based Adaptive Fuzzy Fault-Tolerant Control for Nonlinear Systems Using Small-Gain Approach. Int. J. Fuzzy Syst. 21, 685–699 (2019). https://doi.org/10.1007/s40815-019-00607-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00607-z

Keywords

Search

Navigation