Skip to main content
SpringerLink
Log in

Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

In this paper, an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities. The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity. Firstly, a dynamic gain is introduced to deal with the unknown growth rate, and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse. Then, by virtue of hyperbolic functions and sign functions, a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system. Moreover, the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy. Finally, two simulation examples are given to verify the effectiveness of the control 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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Hua, C., Gang, F., & Guan, X. (2008). Robust controller design of a class of nonlinear time delay systems via backstepping method. Automatica, 44(2), 567–573. https://doi.org/10.1016/j.automatica.2007.06.008

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhou, B., & Yang, X. (2018). Global stabilization of feedforward nonlinear time-delay systems by bounded controls. Automatica, 88, 21–30. https://doi.org/10.1016/j.automatica.2017.10.021

    Article  MathSciNet  MATH  Google Scholar 

  3. Li, H., Zhang, X., & Hou, T. (2019). Output feedback control of large-scale nonlinear time-delay systems with unknown measurement sensitivities. IET Control Theory and Applications, 13(13), 2122–2127. https://doi.org/10.1049/iet-cta.2018.5501

    Article  MathSciNet  Google Scholar 

  4. Zhang, X., Baron, L., Liu, Q., & Boukas, E.-K. (2011). Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems. IEEE Transactions on Automatic Control, 56(3), 692–697. https://doi.org/10.1109/TAC.2010.2097150

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang, X., Liu, L., Feng, G., & Zhang, C. (2013). Output feedback control of large-scale nonlinear time-delay systems in lower triangular form. Automatica, 49(11), 3476–3483. https://doi.org/10.1016/j.automatica.2013.08.026

  6. Seto, D., & Baillieul, J. (1994). Adaptive control of nonlinear systems with a triangular structure. IEEE Transactions on Automatic Control, 39(7), 1411–1428. https://doi.org/10.1109/9.299624

    Article  MathSciNet  MATH  Google Scholar 

  7. Koo, M.-S., Choi, H.-L., & Lim, J.-T. (2010). Global regulation of a class of uncertain nonlinear systems by switching adaptive controller. IEEE Transactions on Automatic Control, 55(12), 2822–2827. https://doi.org/10.1109/TAC.2010.2069430

    Article  MathSciNet  MATH  Google Scholar 

  8. Lehman, Brad, & Erik, Verriest. (1991). Stability of a continuous stirred reactor with delay in the recycle stream. Proceedings of the IEEE Conference on Decision and Control, 2, 1875–1876, Brighton, UK.

  9. Tran, T.-T., Ge, S. S., & He, W. (2016). Adaptive control for an uncertain robotic manipulator with input saturations. Control Theory and Technology, 14(2), 113–121. https://doi.org/10.1007/s11768-016-5059-0

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, T., Xu, H., Xia, X., & Yi, Y. (2020). Adaptive neural optimal control of uncertain nonlinear systems with output constraint. Neurocomputing, 406, 182–195. https://doi.org/10.1016/j.neucom.2020.04.007

    Article  Google Scholar 

  11. Zhang, W., Yu, Z., & Li, S. (2021). Adaptive output consensus for heterogeneous nonlinear multi-agent systems with multi-type input constraints under switching-directed topologies. Control Theory and Technology, 19(2), 260–272. https://doi.org/10.1007/s11768-020-00029-5

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhou, J., Wen, C., & Wang, W. (2018). Adaptive control of uncertain nonlinear systems with quantized input signal. Automatica, 95, 152–162. https://doi.org/10.1016/j.automatica.2018.05.014

    Article  MathSciNet  MATH  Google Scholar 

  13. Lei, H., & Lin, W. (2007). Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach. Systems and Control Letters, 56(7), 529–537. https://doi.org/10.1016/j.sysconle.2007.03.002

    Article  MathSciNet  MATH  Google Scholar 

  14. Hua, C., Li, Y., Zhang, L., & Guan, X. (2019). Adaptive state feedback control for time-delay stochastic nonlinear systems based on dynamic gain method. International Journal of Control, 92(12), 2806–2819. https://doi.org/10.1080/00207179.2018.1459860

    Article  MathSciNet  MATH  Google Scholar 

  15. Cho, H., & Bai, E. R. W. (1998). Convergence results for an adaptive dead zone inverse. International Journal of Adaptive Control and Signal Processing, 12(5), 451–466. https://doi.org/10.1002/(SICI)1099-1115(199808)12:5<451::AID-ACS504>3.0.CO;2-R

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhou, J. (2008). Decentralized adaptive control for large-scale time-delay systems with dead-zone input. Automatica, 44(7), 1790–1799. https://doi.org/10.1016/j.automatica.2007.10.037

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang, X. S., Su, C. Y., & Hong, H. (2004). Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica, 40(3), 407–413. https://doi.org/10.1016/j.automatica.2003.10.021

    Article  MathSciNet  MATH  Google Scholar 

  18. Ibrir, S., Xie, W., & Su, C. (2007). Adaptive tracking of nonlinear systems with non-symmetric dead-zone input. Automatic, 43(3), 522–530. https://doi.org/10.1016/j.automatica.2006.09.022

    Article  MathSciNet  MATH  Google Scholar 

  19. Hua, C., Wang, Q., & Guan, X. (2008). Adaptive tracking controller design of nonlinear systems with time delays and unknown dead-zone input. IEEE Transactions on Automatic Control, 53(7), 1753–1759. https://doi.org/10.1109/TAC.2008.928324

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, L., Li, H., Zhou, Q., & Lu, R. (2017). Adaptive fuzzy control for nonstrict feedback systems with unmodeled dynamics and fuzzy dead zone via output feedback. IEEE Transactions on Cybernetics, 47(9), 2400–2412. https://doi.org/10.1109/TCYB.2017.2684131

    Article  Google Scholar 

  21. Chen, Y., Liu, Z., Chen, C. L. P., & Zhang, Y. (2021). Adaptive fuzzy control of switched nonlinear systems with uncertain dead-zone: A mode-dependent fuzzy dead-zone model. Neurocomputing, 432, 133–144. https://doi.org/10.1016/j.neucom.2020.12.044

    Article  Google Scholar 

  22. Jia, X., Xu, S., Qi, Z., Zhang, Z., & Chu, Y. (2019). Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input. ISA Transactions, 95, 35–44. https://doi.org/10.1016/j.isatra.2019.05.020

    Article  Google Scholar 

  23. Pongvuthithum, R., Rattanamongkhonkun, K., & Lin, W. (2018). Asymptotic regulation of time-delay nonlinear systems with unknown control directions. IEEE Transactions on Automatic Control, 63(5), 1495–1502. https://doi.org/10.1109/TAC.2017.2748898

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang, Z. Q., Xu, S. Y., & Zhang, B. Y. (2014). Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity. IEEE Transactions on Automatic Control, 59(5), 1336–1341. https://doi.org/10.1109/TAC.2013.2289704

    Article  MathSciNet  MATH  Google Scholar 

  25. Krishnamurthy, P., & Khorrami, F. (2008). Feedforward systems with ISS appended dynamics: Adaptive output-feedback stabilization and disturbance attenuation. IEEE Transactions on Automatic Control, 53(1), 405–412. https://doi.org/10.1109/TAC.2007.914231

    Article  MathSciNet  MATH  Google Scholar 

  26. Xing, L., Wen, C., Liu, Z., Su, H., & Cai, J. (2017). Adaptive compensation for actuator failures with event-triggered input. Automatica, 85, 129–136. https://doi.org/10.1016/j.automatica.2017.07.061

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, Shandong, China

    Minghui Feng, Yanjie Chang, Zhiyu Duan & Xianfu Zhang

Authors
  1. Minghui Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanjie Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiyu Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xianfu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianfu Zhang.

Additional information

The work was supported by the National Natural Science Foundation of China (Nos. 61973189, 62073190), the Research Fund for the Taishan Scholar Project of Shandong Province of China (No. ts20190905), and the Natural Science Foundation of Shandong Province of China (No. ZR2020ZD25).

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

Feng, M., Chang, Y., Duan, Z. et al. Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input. Control Theory Technol. 21, 530–540 (2023). https://doi.org/10.1007/s11768-023-00140-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-023-00140-3

Keywords

Search

Navigation