Skip to main content
SpringerLink
Log in

Adaptive Fuzzy Variable Structure Control of Fractional-Order Nonlinear Systems with Input Nonlinearities

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

Abstract

The unknown dead-zone input nonlinearities (DZINs) are considered in the Riemann–Liouville fractional-order nonlinear systems (FONSs) and the Caputo FONSs in this paper. The unknown DZINs in the FONSs will cause FONSs instability. In this paper, by using the fractional-order Lyapunov stability theory, a variable structure adaptive fuzzy control (AFC) scheme is designed to solve the unknown DZINs in the FONSs. The unknown terms of the FONSs and the uncertain terms of DZINs are handled by fuzzy logic systems (FLSs). The parameters boundedness of FLSs is guaranteed via the constructed fractional-order adaptive laws (FOALs). By using FLSs, this paper does not need to know the exact values of gain reduction tolerances (GRTs) in the unknown DZINs, which makes the constructed scheme more suitable for the actual system. The scheme proposed in this paper can be used to effectively control the Riemann–Liouville FONSs and the Caputo FONSs with/without unknown DZINs. Finally, three simulation results verify the AFCs we designed are effective for both Riemann–Liouville FONSs and Caputo FONSs with unknown DZINs.

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

Similar content being viewed by others

References

  1. Shen, J., Lam, J.: Stability and performance analysis for positive fractional-order systems with time-varying delays. IEEE Trans. Automat. Control 61(9), 2676–2681 (2015)

    Article  MathSciNet  Google Scholar 

  2. Kaczorek, T.: Positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems. Int. J. Nonlinear Sci. Numer. Simul. 19, 299–307 (2018)

    Article  MathSciNet  Google Scholar 

  3. Sweilam, N.H., Almekhlafi, S.M., Albalawi, A.O.: A novel variable-order fractional nonlinear Klein Gordon model: a numerical approach. Numer. Methods Part. Differ. Eq. 35(5), 1617–1629 (2019)

    Article  MathSciNet  Google Scholar 

  4. Ha, S., Liu, H., Li, S., Liu, A.: Backstepping-based adaptive fuzzy synchronization control for a class of fractional-order chaotic systems with input saturation. Int. J. Fuzzy Syst. 21(5), 1571–1584 (2019)

    Article  MathSciNet  Google Scholar 

  5. Haruna, A., Mohamed, Z., Efe, M.O., Basri, M.A.M.: Improved integral backstepping control of variable speed motion systems with application to a laboratory helicopter. ISA Trans. 97, 1–13 (2020)

    Article  Google Scholar 

  6. Mirzajani, S., Aghababa, M.P., Heydari, A.: Adaptive control of nonlinear fractional-order systems using T–S fuzzy method. Int. J. Mach. Learn. Cybernet. 10(3), 527–540 (2019)

    Article  Google Scholar 

  7. Liu, H., Pan, Y., Cao, J., Zhou, Y., Wang, H.: Positivity and stability analysis for fractional-order delayed systems: a T–S fuzzy model approach. IEEE Trans. Fuzzy Syst. (2020)

  8. Efe, M.O.: Fractional fuzzy adaptive sliding mode control of a 2-DOF direct-drive robot arm. Syst. Man Cybernet. 38(6), 1561–1570 (2008)

    Article  Google Scholar 

  9. Muñoz-Vázquez, A.J., Ortiz-Moctezuma, M.B., Sánchez-Orta, A., Parra-Vega, V.: Adaptive robust control of fractional-order systems with matched and mismatched disturbances. Math. Comput. Simul. 162, 85–96 (2019)

    Article  MathSciNet  Google Scholar 

  10. Dabiri, A., Butcher, E.A.: Optimal observer-based feedback control for linear fractional-order systems with periodic coefficients. J. Vibrat. Control 25(7), 1379–1392 (2019)

    Article  MathSciNet  Google Scholar 

  11. Bingi, K., Ibrahim, R., Karsiti, M.N., Hassan, S.M., Harindran, V.R.: Scilab based toolbox for fractional-order systems and PID controllers. Springer, New York (2020)

    Book  Google Scholar 

  12. Efe, M.O., Kasnakoglu, C.: A fractional adaptation law for sliding mode control. Int. J. Adapt. Control Signal Process. 22(10), 968–986 (2008)

    Article  MathSciNet  Google Scholar 

  13. Aghababa, M.P.: Robust stabilization ANS synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Commun. Nonlinear Sci. Numer. Simulat. 17(6), 2670–2681 (2012)

    Article  MathSciNet  Google Scholar 

  14. Ramli, L., Mohamed, Z., Efe, M.O., Lazim, I.M., Jaafar, H.I.: Efficient swing control of an overhead crane with simultaneous payload hoisting and external disturbances. Mech. Syst. Signal Process. 135, 106326 (2020)

    Article  Google Scholar 

  15. Baleanu, D., Jajarmi, A., Sajjadi, S.S., Mozyrska, D.: A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos 29(8), 083127 (2019)

    Article  MathSciNet  Google Scholar 

  16. Boulkroune, A., Tadjine, M., Msaad, M., Farza, M.: Design of a unified adaptive fuzzy observer for uncertain nonlinear systems. Inform. Sci. 265, 139–153 (2014)

    Article  MathSciNet  Google Scholar 

  17. Kalat, A.A.: A robust direct adaptive fuzzy control for a class of uncertain nonlinear MIMO systems. Soft Comput. 23(19), 9747–9759 (2019)

    Article  Google Scholar 

  18. Pan, Y., Sun, T., Yu, H.: On parameter convergence in least squares identification and adaptive control. Int. J. Robust Nonlinear Control 29(10), 2898–2911 (2019)

    Article  MathSciNet  Google Scholar 

  19. Kaczorek, T.: Global stability of nonlinear feedback systems with positive descriptor linear parts. Bull. Polish Acad. Sci.-Tech. Sci. 67(1), 45–51 (2019)

    Google Scholar 

  20. Han, Z., Li, S., Liu, H.: Composite learning sliding mode synchronization of chaotic fractional-order neural networks. J. Adv. Res. (2020). https://doi.org/10.1016/j.jare.2020.04.006.

  21. Ha, S., Liu, H., Li, S.: Adaptive fuzzy back stepping control of fractional-order chaotic systems with input saturation. J. Intell. Fuzzy Syst 37(5), 6513–6525 (2019)

    Article  Google Scholar 

  22. Pinto, C.M.A., Carvalho, A.R.M.: Diabetes mellitus and TB co-existence: clinical implications from a fractional-order modelling. Appl. Math. Modell. 68, 219–243 (2019)

    Article  MathSciNet  Google Scholar 

  23. Li, Y., Qu, F., Tong, S.: Observer-based fuzzy adaptive finite-time containment control of nonlinear multiagent systems with input delay. IEEE Trans. Syst. Man Cybernet. (2020)

  24. Li, T., Tong, S., Feng, G.: A novel robust adaptive fuzzy tracking control for a class of nonlinear multi-input/multi-output systems. IEEE Trans. Fuzzy Syst. 18(1), 150–160 (2009)

    Google Scholar 

  25. Song, X., Men, Y., Zhou, J., Zhao, J., Shen, H.: Event-triggered H\(\infty \) control for networked discrete-time markov jump systems with repeated scalar nonlinearities. Appl. Math. Comput. 298, 123–132 (2017)

    MathSciNet  MATH  Google Scholar 

  26. Kumar, D., Singh, J., Tanwar, K., Baleanu, D.: A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and mittag-leffler laws. Int. J. Heat. Mass Trans. 138, 1222–1227 (2019)

    Article  Google Scholar 

  27. Ha, S., Chen, L., Liu, H.: Command filtered adaptive neural network synchronization control of fractional-order chaotic systems subject to unknown dead zones. J. Franklin Inst. (2021). https://doi.org/10.1016/j.jfranklin.2021.02.012

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

    Article  MathSciNet  Google Scholar 

  29. Tong, S., Li, Y., Sui, S.: Adaptive fuzzy output feedback control for switched nonstrict-feedback nonlinear systems with input nonlinearities. IEEE Trans. Fuzzy Syst. 24(6), 1426–1440 (2016)

    Article  Google Scholar 

  30. Sun, Y., Chen, L., Qin, H., Wang, W.: Distributed finite-time coordinated tracking control for multiple euler-lagrange systems with input nonlinearity. Nonlinear Dyn. 95(3), 2395–2414 (2019)

    Article  Google Scholar 

  31. Roohi, M., Aghababa, M.P., Haghighi, A.R.: Switching adaptive controllers to control fractional-order complex systems with unknown structure and input nonlinearities. Complexity 21(2), 211–223 (2015)

    Article  MathSciNet  Google Scholar 

  32. Liu, H., Li, S., Wang, H., Sun, Y.: Adaptive fuzzy control for a class of unknown fractional-order neural networks subject to input nonlinearities and dead-zones. Inform. Sci. 454, 30–45 (2018)

    Article  MathSciNet  Google Scholar 

  33. Boulkroune, A., Tadjine, M., MSaad, M., Farza, M.: Fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction. Fuzzy sets Syst. 161(6), 797–820 (2010)

    Article  MathSciNet  Google Scholar 

  34. Liu, H., Li, S., Li, G., Wang, H.: Adaptive controller design for a class of uncertain fractional-order nonlinear systems: an adaptive fuzzy approach. Int. J. Fuzzy Syst 20(2), 366–379 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61967001, in part by the Guangxi Natural Science Foundation under Grant 2019GXNSFAA185007, and in part by the Xiangsihu Young Scholars Innovative Research Team of Guangxi University for Nationalities under Grant 2019RSCXSHQN02.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Shumin Ha & Liangyun Chen

  2. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China

    Heng Liu

Authors
  1. Shumin Ha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liangyun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heng Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ha, S., Chen, L. & Liu, H. Adaptive Fuzzy Variable Structure Control of Fractional-Order Nonlinear Systems with Input Nonlinearities. Int. J. Fuzzy Syst. 23, 2309–2323 (2021). https://doi.org/10.1007/s40815-021-01105-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01105-x

Keywords

Search

Navigation