Skip to main content
SpringerLink
Log in

Adaptive Asymptotic Tracking of Nonlinear Systems Using Nonlinearly Parameterized First-Order Sugeno Fuzzy Approximator

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

Abstract

In this paper, an adaptive tracking control scheme is presented for a class of nonlinear systems using nonlinearly parameterized first-order Sugeno fuzzy approximator. The parameters in the first-order Sugeno consequents and Gaussian basis functions are assumed to be unknown. First, based on the parameterization of the exponential function, a new parameterization model of first-order Sugeno fuzzy system is developed. The new representation of unknown system function is constructed by exploiting the signal replace approach. Then, unknown fuzzy parameters and known functions with the tracking elements being arguments are collected, respectively, and some new parameters and useful functions are defined, respectively. Furthermore, adaptive controller is designed and analyzed. Global boundedness of the closed-loop system is established, and asymptotic tracking is achieved. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.

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

Similar content being viewed by others

References

  1. Alata, M., Su, C.Y., Demirli, K.: Adaptive control of a class of nonlinear systems with a first-order parameterized sugeno fuzzy approximator. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 31(3), 410–419 (2001)

    Article  Google Scholar 

  2. Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Trans. Fuzzy Syst. 18(5), 883–892 (2010)

    Article  Google Scholar 

  3. Chen, W., Zhang, Z.: Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign. Fuzzy Sets Syst. 161(6), 821–836 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Demirli, K., Muthukumaran, P.: Fuzzy system identification with higher order subtractive clustering. J. Intell. Fuzzy Syst. 9(3, 4), 129–158 (2000)

    Google Scholar 

  5. Han, H., Su, C.Y.: Robust fuzzy control of nonlinear systems using shape-adaptive radial basis functions. Fuzzy Sets Syst. 125(1), 23–38 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Han, H., Su, C.Y., Stepanenko, Y.: Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators. IEEE Trans. Fuzzy Syst. 9(2), 315–323 (2001)

    Article  Google Scholar 

  7. Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Upper Saddle River (1996)

    MATH  Google Scholar 

  8. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)

    MATH  Google Scholar 

  9. Li, Y., Tong, S., Li, T.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299–2308 (2014)

    Article  Google Scholar 

  10. Poggio, T., Girosi, F.: Networks for approximation and learning. Proce. IEEE 78(9), 1481–1497 (1990)

    Article  MATH  Google Scholar 

  11. Polycarpou, M.M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41(3), 447–451 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Su, C.Y., Stepanenko, Y.: Adaptive control of a class of nonlinear systems with fuzzy logic. IEEE Trans. Fuzzy Syst. 2(4), 285–294 (1994)

    Article  Google Scholar 

  13. Tong, S., Zhang, L., Li, Y.: Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 37–47 (2016)

    Article  Google Scholar 

  14. Wang, H., Liu, P.X., Shi, P.: Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems. IEEE Trans. Cybern. 47(9), 2568–2578 (2017)

    Article  Google Scholar 

  15. Wang, H., Liu, W., Qiu, J., Liu, P.X.: Adaptive fuzzy decentralized control for a class of strong interconnected nonlinear systems with unmodeled dynamics. IEEE Trans. Fuzzy Syst. (2017). https://doi.org/10.1109/TFUZZ.2017.2694799

    Google Scholar 

  16. Wang, H., Shi, P., Li, H., Zhou, Q.: Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Trans. Cybern. (2017). https://doi.org/10.1109/TCYB.2016.2607166

    Google Scholar 

  17. 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 

  18. Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1, 146–155 (1993)

    Article  Google Scholar 

  19. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability. Prentice-Hall, Upper Saddle River (1994)

    Google Scholar 

  20. Wang, L.X.: Stable adaptive fuzzy controllers with application to inverted pendulum tracking. IEEE Trans. Syst. Man Cybern. Part B Cybern. 26(5), 677–691 (1996)

    Article  Google Scholar 

  21. Wang, M., Zhang, Z.: Globally adaptive asymptotic tracking control of nonlinear systems using nonlinearly parameterized fuzzy approximator. J. Franklin Inst. 352(7), 2783–2795 (2015)

    Article  MathSciNet  Google Scholar 

  22. Ying, H.: Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 28(4), 515–520 (1998)

    Article  Google Scholar 

  23. Zhang, Z., Xu, S., Zhang, B.: Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity. IEEE Trans. Autom. Control 59(11), 1336–1341 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang, Z., Xu, S., Zhang, B.: Exact tracking control of nonlinear systems with time delays and dead-zone input. Automatica 52(52), 272–276 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhao, X., Yang, H., Xia, W., Wang, X.: Adaptive fuzzy hierarchical sliding mode control for a class of MIMO nonlinear time-delay systems with input saturation. IEEE Trans. Fuzzy Syst. (2017). https://doi.org/10.1109/TFUZZ.2016.2594273

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61473171 and 61374090, Shandong Provincial Natural Science Foundation for Distinguished Young Scholars under Grant JQ201515, Shandong Provincial Natural Science Foundation under Grant ZR2017MF063 and the Taishan Scholarship Project of Shandong Province under Grant tsqn20161032.

Author information

Authors and Affiliations

  1. Key Laboratory of Power System Intelligent Dispatch and Control of the Ministry of Education, Shandong University, Jinan, 250061, China

    Maoli Wang

  2. School of Engineering, Qufu Normal University, Rizhao, 276826, China

    Zhengqiang Zhang, Qiangde Wang & Hanyong Shao

  3. Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan, 250014, China

    Maoli Wang

Authors
  1. Maoli Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengqiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiangde Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hanyong Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhengqiang Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, M., Zhang, Z., Wang, Q. et al. Adaptive Asymptotic Tracking of Nonlinear Systems Using Nonlinearly Parameterized First-Order Sugeno Fuzzy Approximator. Int. J. Fuzzy Syst. 20, 1079–1087 (2018). https://doi.org/10.1007/s40815-017-0416-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0416-9

Keywords

Search

Navigation