Skip to main content
SpringerLink
Log in

Fixed-Time Fuzzy Adaptive Tracking Control for High-Order Systems with Unknown Nonlinearities and Control Directions

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

Abstract

This paper presents a fixed-time tracking controller for a class of high-order nonlinear systems with completely unknown nonlinearities and unknown control directions. To perform the high-order practical tracking control objective, which is quite different from both the low-order control ones and the asymptotic stabilization ones, a coordinate transformation related to tracking error is introduced to make the tracking error be constrained to a prescribed interval including the origin in a fixed time by employing a finite-time stable function. A unique adaptive parameter is adopted to approximate the unknown nonlinear functions by applying fuzzy logic functions. Nussbaum functions are utilized to determine the unknown control directions. Based on the domination technique and the method of adding a power integrator, the provided controller can guarantee all the states of the closed-loop systems and control signal are bounded. Three simulation examples show the feasibility and efficiency of the proposed tracking control strategy.

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
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, Englewood Cliffs (2012)

    Google Scholar 

  2. Ilchmann, A., Ryan, E.P.: Universal \(\lambda\)-tracking for nonlinearly perturbed systems in the presence of noise. Automatica 30(2), 337–346 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wang, N., Qian, C.J., Sun, Z.Y.: Global asymptotic output tracking of nonlinear second-order systems with power integrators. Automatica 80(6), 156–161 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, Z.Q., Xu, S.Y., Zhang, B.Y.: Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity. IEEE Trans. Automatica Control 59(5), 1336–1341 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ye, X.D., Ding, Z.: Robust tracking control of uncertain nonlinear systems with unknown control directions. Syst. Control Lett. 42(1), 1–10 (2001)

    Article  MathSciNet  Google Scholar 

  6. Gong, Q., Qian, C.J.: Global practical tracking of a class of nonlinear systems by output feedback. Automatica J. IFAC 43, 184–189 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhai, J.Y., Fei, S.M.: Global practical tracking control for a class of uncertain non-linear systems. IET Control Theory Appl. 5(11), 1343–1351 (2011)

    Article  MathSciNet  Google Scholar 

  8. Yu, J.B., Zhao, Y., Wu, Y.Q.: Global robust output tracking control for a class of uncertain cascaded nonlinear systems. Automatica 93(7), 274–281 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, W.Q., Liu, L., Feng, G.: Distributed output-feedback tracking of multiple nonlinear systems with unmeasurable states. IEEE Trans. Syst. Man Cybern. 51(1), 477–486 (2018)

    Article  Google Scholar 

  10. Gao, Y.B., Liu, G.X., Wang, Z.H., Wu, L.G.: Interval type-2 FNN-based quantized tracking control for hypersonic flight vehicles with prescribed performance. IEEE Trans. Syst. Man Cybern. 51(3), 1981–1993 (2021)

    Google Scholar 

  11. Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6), 1530–1535 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, K., Xu, T., Xu, H., Chen, L.: Adaptive swarm control for the high-order self-organized system with unknown nonlinear dynamics and unmeasured states. Int. J. Fuzzy Syst. 24, 391–404 (2022)

    Article  Google Scholar 

  13. Li, Y.M., Shao, X.F., Tong, S.C.: Adaptive fuzzy prescribed performance control of nontriangular structure nonlinear systems. IEEE Trans. Fuzzy Syst. 28(10), 2416–2426 (2020)

    Article  Google Scholar 

  14. Sun, Z.Y., Shao, Y., Chen, C.C.: Fast finite-time stability and its application in adaptive control of high-order nonlinear system. Automatica 106(5), 339–348 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sun, W., Su, S.F., Wu, Y.Q., Xia, J.W.: A novel adaptive fuzzy control for output constrained stochastic nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 29(5), 1188–1197 (2021)

    Article  Google Scholar 

  16. Liu, X.P., Wang, H.Q., Gao, C., Chen, M.: Adaptive fuzzy funnel control for a class of strict feedback nonlinear systems. Neurocomputing 241(7), 71–80 (2017)

    Article  Google Scholar 

  17. Man, Y.C., Liu, Y.G.: Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers. Automatica 100, 171–181 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, X.C., Wang, T.Y.: Elastic and reliable bandwidth reservation based on distributed traffic monitoring and control. IEEE Trans. Parallel Distrib. Syst. 33(12), 4563–4580 (2022)

    Article  Google Scholar 

  19. Li, H.Y., Zhao, S.Y., He, W., Lu, R.Q.: Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone. Automatica 100(2), 99–107 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sun, W., Wu, Y.Q., Sun, Z.Y.: Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 28(12), 3161–3170 (2020). https://doi.org/10.1109/TFUZZ.2020.2967295

    Article  Google Scholar 

  21. Tang, Z.L., Ge, S.S., Tee, K.P., He, W.: Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints. IEEE Trans. IEEE Trans. Syst. Man Cybern. 46(12), 1618–1629 (2016)

    Article  Google Scholar 

  22. Huang, J.S., Wang, W., Wen, C.Y., Zhou, J.: Adaptive control of a class of strict-feedback time-varying nonlinear systems with unknown control coefficients. Automatica 93(7), 98–105 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  23. Li, D.J., Li, D.P.: Adaptive tracking control for nonlinear time varying delay systems with full state constraints and unknown control coefficients. Automatica 93(7), 444–453 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang, T., Tong, S.C., Li, Y.M.: Robust adaptive fuzzy output feedback control for stochastic nonlinear systems with unknown control direction. Neurocomputing 106(4), 31–41 (2013)

    Article  Google Scholar 

  25. Wang, L.J., Chen, C.L.P.: Adaptive fuzzy dynamic surface control of nonlinear constrained systems with unknown virtual control coefficients. IEEE Trans. Fuzzy Syst. 28(8), 1737–1747 (2019). https://doi.org/10.1109/TFUZZ.2019.2921277

    Article  MathSciNet  Google Scholar 

  26. Wai, R.J., Lin, Y.W.: Adaptive moving-target tracking control of a vision-based mobile robot via a dynamic petri recurrent fuzzy neural network. IEEE Trans. Fuzzy Syst. 21(4), 688–701 (2013)

    Article  Google Scholar 

  27. Sun, Z.Y., Liu, C.Y., Su, S.F., Sun, W.: Global finite-time stabilization for uncertain systems with unknown measurement sensitivity. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2020.3041923

    Article  Google Scholar 

  28. Liu, Y., Liu, X.P., Jing, Y.W., Zhang, Z.Y.: A Novel finite-time adaptive fuzzy tracking control scheme for nonstrict feedback systems. IEEE Trans. Fuzzy Syst. 27(4), 646–658 (2018)

    Article  Google Scholar 

  29. Qian, C.J., Lin, W.: Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  30. Sun, Z.Y., Liu, Y.G.: Adaptive practical output tracking control for high-order nonlinear uncertain systems. Acta Automatica Sinaca 34(8), 984–989 (2008)

    Article  MathSciNet  Google Scholar 

  31. Sun, Z.Y., Peng, Y.R., Wen, C.Y., Chen, C.C.: Fast finite-time adaptive stabilization of high-order uncertain nonlinear system with an asymmetric output constraint. Automatica 121(11), 109170 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  32. Xue, L.L., Zhang, T.L., Zhang, W.H.: Global adaptive stabilization and tracking control for high-order stochastic nonlinear systems with time-varying delays. IEEE Trans. Autom. Control 10(9), 1109–1117 (2018)

    MathSciNet  MATH  Google Scholar 

  33. Feng, S.S., Sun, Z.Y., Zhou, C.Q., Chen, ChCh., Meng, Q.H.: Output tracking control via neural networks for high-order stochastic nonlinear systems with dynamic uncertainties. Int. J. Fuzzy Syst. 23(3), 716–726 (2021)

    Article  Google Scholar 

  34. Ma, H., Liang, H.J., Zhou, Q., Ahn, C.K.: Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances. IEEE Trans. Syst. Man Cybern. 49(3), 506–515 (2019)

    Article  Google Scholar 

  35. Sun, Z.Y., Yun, M.M., Li, T.: A new approach to fast global finite-time stabilization of high-order nonlinear system. Automatica 81, 455–463 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  36. Yu, L.Y., Sun, Z.Y., Meng, Q.H., Chen, Z.Q.: A new finite-time stabilizing design for a class of high-order uncertain nonlinear systems and its application in maglev systems. IEEE Trans. Syst. Man Cybern. (2022). https://doi.org/10.1109/TSMC.2022.3182395

    Article  Google Scholar 

  37. Li, B.M., Xia, J.W., Su, S.F., Sun, W., Zhang, H.S., Liang, J., Zhou, Q., Ahn, C.K.: Event-triggered adaptive fuzzy tracking control for nonlinear systems with unknown control directions. IEEE Trans. Syst. Man Cybern. 52(7), 4648–4657 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported in part by National Natural Science Foundation of China (62173208), Taishan Scholar Project of Shandong Province of China (tsqn202103061), Shandong Qingchuang Science and Technology Program of Universities (2019KJN036), Zhejiang Provincial Natural Science Foundation of China (LZ21E050002), and the Ministry of Science and Technology (MOST), Taiwan, under Grant MOST 111-2221-E-006-204-MY2.

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Application Technology, Jining University, Qufu, 273155, Shandong, People’s Republic of China

    Le-Yuan Yu

  2. Institute of Automation, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    Zong-Yao Sun & Jiao-Jiao Li

  3. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Qing-hua Meng

  4. Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Chih-Chiang Chen

Authors
  1. Le-Yuan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zong-Yao Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qing-hua Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chih-Chiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiao-Jiao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zong-Yao Sun.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, LY., Sun, ZY., Meng, Qh. et al. Fixed-Time Fuzzy Adaptive Tracking Control for High-Order Systems with Unknown Nonlinearities and Control Directions. Int. J. Fuzzy Syst. 25, 1546–1558 (2023). https://doi.org/10.1007/s40815-022-01456-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-022-01456-z

Keywords

Search

Navigation