Skip to main content
SpringerLink
Log in

Fuzzy Adaptive Control of Nonlinear Systems with Odd System Powers, Complex Dynamics, and Uncertain Control Coefficients

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

Abstract

The adaptive stabilization issue for complicated nonlinear systems is investigated in this work. The discussed problem is comparatively challenging since the system owns non-triangular structure and involves unknown coefficients, unknown parameters, and complex dynamics. By proposing an improved fuzzy-based adaptive control approach, a new stable control law is designed to make semi-globally uniformly ultimately bounded (SUUB). The presented method is validated with a simulation example.

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

Similar content being viewed by others

References

  1. Sun, W., Su, S.F., Xia, J., Nguyen, V.T.: Adaptive fuzzy tracking control of flexible-joint robots with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. 49(11), 2201–2209 (2018)

    Article  Google Scholar 

  2. Machowski, J., Lubosny, Z., Bialek, J.W., et al.: Power System Dynamics: Stability and Control. Wiley, New York (2020)

    Google Scholar 

  3. Martínez-Guerra, R., Cruz-Ancona, C.D.: Algorithms of Estimation for Nonlinear Systems. Springer International Publishing AG, New York (2017)

    Book  Google Scholar 

  4. Khalil, H.K., Grizzle, J.W.: Nonlinear Systems. Prentice hall, Upper Saddle River, NJ (2002)

    Google Scholar 

  5. Zong, G., Ren, H., Karimi, H.R.: Event-triggered communication and annular finite-time \(H\infty \) filtering for networked switched systems. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3010917

    Article  Google Scholar 

  6. Jiao, T., Zheng, W., Xu, S.: Unified stability criteria of random nonlinear time-varying impulsive switched systems. IEEE Trans. Circ. Syst. I Regul. Pap. 67(9), 3099–3112 (2020)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  8. Astolfi, A., Karagiannis, D., Ortega, R.: Nonlinear and Aadaptive Control with Applications. Springer Science & Business Media, New York (2007)

    MATH  Google Scholar 

  9. Koshkouei, A.J., Zinober, A.S.I., Burnham, K.J.: Adaptive sliding mode backstepping control of nonlinear systems with unmatched uncertainty. Asian J. Control 6(4), 447–453 (2004)

    Article  Google Scholar 

  10. Wang, C., Wu, Y., Yu, J.: Barrier Lyapunov functions-based dynamic surface control for pure-feedback systems with full state constraints. IET Control Theory Appl. 11(4), 524–530 (2016)

    Article  MathSciNet  Google Scholar 

  11. Benabdallah, A., Ayadi, H., Mabrouk, M.: Global adaptive output stabilization of uncertain nonlinear systems with polynomial output depending growth rate. Int. J. Adapt. Control Signal Process. 28(7–8), 604–619 (2014)

    Article  MathSciNet  Google Scholar 

  12. Li, Y., Li, K., Tong, S.: Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems. IEEE Trans. Fuzzy Syst. 27(1), 96–110 (2018)

    Article  Google Scholar 

  13. Li, Y., Yang, T., Tong, S.: Adaptive neural networks finite-time optimal control for a class of nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2955438

    Article  Google Scholar 

  14. Lin, W., Qian, C.: Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique. Syst. Control Lett. 39(5), 353–364 (2000)

    Article  MathSciNet  Google Scholar 

  15. Zhang, W., Xue, L.R., Liu, Z., Sun, Z.: Global stabilisation for a class of upper-triangular nonlinear systems with unmodelled dynamics and time-delay. Int. J. Control 93(5), 1147–1158 (2020)

    Article  MathSciNet  Google Scholar 

  16. Jo, H.W., Choi, H.L., Lim, J.T.: Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain. Syst. Control Lett. 71, 44–53 (2014)

    Article  MathSciNet  Google Scholar 

  17. Marconi, L., Isidori, A.: Robust global stabilization of a class of uncertain feedforward nonlinear systems. Syst. Control Lett. 41(4), 281–290 (2000)

    Article  MathSciNet  Google Scholar 

  18. Zhao, X., Shi, P., Zheng, X., Zhang, J.: Intelligent tracking control for a class of uncertain high-order nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 27(9), 1976–1982 (2015)

    Article  MathSciNet  Google Scholar 

  19. Sun, W., Su, S.F., Dong, G., Bai, W.: Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2898204

    Article  Google Scholar 

  20. Sun, W., Su, S., Wu, Y., Nguyen, V.: Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. 50(8), 3424–3432 (2020)

    Article  Google Scholar 

  21. Sun, W., Su, S., Liu, Z., Sun, Z.: Adaptive intelligent control for input and output constrained high-order uncertain nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2956063

    Article  Google Scholar 

  22. Zha, W., Qian, C., Yan, S.: Controller design for a class of nontriangular nonlinear systems with input dependent growth rate. Int. J. Robust Nonlinear Control 29(5), 1325–1338 (2019)

    Article  MathSciNet  Google Scholar 

  23. Krishnamurthy, P., Khorrami, F.: Generalized state scaling and applications to feedback, feedforward, and nontriangular nonlinear systems. IEEE Trans. Autom. Control 52(1), 102–108 (2007)

    Article  MathSciNet  Google Scholar 

  24. Koo, M.S., Choi, H.L.: Regulation of lower triangular and non-triangular nonlinear systems with uncertain high-order nonlinearities via dynamic gain control. Int. J. Robust Nonlinear Control 27(2), 347–360 (2017)

    Article  MathSciNet  Google Scholar 

  25. Su, Z., Qian, C., Shen, J.: Interval homogeneity-based control for a class of nonlinear systems with unknown power drifts. IEEE Trans. Autom. Control 62(3), 1445–1450 (2016)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  27. Chen, C., Sun, Z.: A unified approach to finite-time stabilization of high-order nonlinear systems with an asymmetric output constraint. Automatica 111, 108581 (2020)

    Article  MathSciNet  Google Scholar 

  28. Lan, Q., Zhang, C., Li, S.: Global decentralised stabilisation for a class of uncertain large-scale high-order upper-triangular nonlinear systems. Int. J. Syst. Sci. 48(6), 1123–1135 (2017)

    Article  MathSciNet  Google Scholar 

  29. Yu, J., Lv, H., Wu, Y.: Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients. Int. J. Adapt. Control Signal Process. 30(6), 843–863 (2016)

    Article  MathSciNet  Google Scholar 

  30. Krishnamurthy, P., Khorrami, F.: A general dynamic scaling based control redesign to handle input unmodeled dynamics in uncertain nonlinear systems. IEEE Trans. Autom. Control 62(9), 4719–4726 (2016)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  32. Wang, F., Chen, B., Liu, X., et al.: Finite-time adaptive fuzzy tracking control design for nonlinear systems. IEEE Trans. Fuzzy Syst. 26(3), 1207–1216 (2017)

    Article  Google Scholar 

  33. Zhou, Q., Wu, C., Shi, P.: Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation. Fuzzy Sets Syst. 316, 49–68 (2017)

    Article  MathSciNet  Google Scholar 

  34. Niu, B., Liu, L., Liu, Y.: Adaptive backstepping-based fuzzy tracking control scheme for output-constrained nonlinear switched lower triangular systems with time-delays[J]. Neurocomputing 175, 759–767 (2016)

    Article  Google Scholar 

  35. Chen, B., Liu, X., Liu, K., et al.: Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Inf. Sci. 180(5), 776–792 (2010)

    Article  MathSciNet  Google Scholar 

  36. Lu, Y.: Adaptive-fuzzy control compensation design for direct adaptive fuzzy control. IEEE Trans. Fuzzy Syst. 26(6), 3222–3231 (2018)

    Article  Google Scholar 

  37. Lin, W., Qian, C.: Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework. IEEE Trans. Autom. Control 47(5), 757–774 (2002)

    Article  MathSciNet  Google Scholar 

  38. Tong, S., Li, Y., Li, Y., et al.: Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 41(6), 1693–1704 (2011)

    Article  Google Scholar 

  39. Xia, J., Li, B., Su, S.F., et al.: Finite-time command filtered event-triggered adaptive fuzzy tracking control for stochastic nonlinear systems. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2985638

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (STIP) (Grant Number: 2019L0011), Youth science and technology research fund of the Shanxi Science and Technology Department of China (Grant Numbers: 201801D221166 and 201801D221167).

Author information

Authors and Affiliations

  1. School of Automation and Software Engineering, Shanxi University, Taiyuan, 030006, China

    Zhen-Guo Liu, Yu-Yuan Shi & Lin-Xian Liu

Authors
  1. Zhen-Guo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu-Yuan Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin-Xian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhen-Guo Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, ZG., Shi, YY. & Liu, LX. Fuzzy Adaptive Control of Nonlinear Systems with Odd System Powers, Complex Dynamics, and Uncertain Control Coefficients. Int. J. Fuzzy Syst. 23, 1257–1266 (2021). https://doi.org/10.1007/s40815-020-01028-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-01028-z

Keywords

Search

Navigation