Skip to main content
SpringerLink
Log in

Command-filtered-based technique for a class of nonlinear systems with finite-time observer in the presence of mismatched disturbances

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper considers the stabilization problem for a class of nonlinear systems in the presence of mismatched disturbances. To achieve this, a differentiator is defined using virtual controls and modified error compensation signals, and the output of the system is asymptotically stabilized by a command-filtered backstepping control scheme combined with a mismatched finite-time disturbance observer. In the employed disturbance observer, the imposed external disturbances are identified precisely within the finite-time period. This produces a better transient performance compared to the Lyapunov parameter estimation method. In addition, a wider range of disturbances can be included as the common restrictive condition is no longer applied to the first derivatives of disturbances. Apart from the functionalities of the employed disturbance observer, the proposed control scheme addresses the problem of the explosion of complexity caused by higher-order differentiation. As a result, when applied to a more complicated system, this method can significantly reduce the complexity of calculation. In the final step, by means of the common Lyapunov function, the finite-time estimation process of the disturbance observer and the asymptotic stability of the given control scheme is shown. Finally, a simulation example is provided to show the effectiveness of the theoretical developments.

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

Similar content being viewed by others

Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

References

  1. Asadollahi, M., Ghiasi, A.R., Badamchizadeh, M.A.: Adaptive control for a class of nonlinear chaotic systems with quantized input delays. J. Frankl. Inst. 357(1), 254–278 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  2. Xu, C., Tang, X., Lü, H., Alfaro-Bittner, K., Boccaletti, S., Perc, M., Guan, S.: Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators. Phys. Rev. Res. 3(4), 043004 (2021)

    Article  Google Scholar 

  3. Tao, L., Chen, Q., Nan, Y.: Disturbance-observer based adaptive control for second-order nonlinear systems using chattering-free reaching law. Int. J. Control Autom. Syst. 17(2), 356–369 (2019)

    Article  Google Scholar 

  4. Mirzaei, M.J., Aslmostafa, E., Asadollahi, M., Badamchizadeh, M.A.: Finite-time synchronization control for a class of perturbed nonlinear systems with fixed convergence time and hysteresis quantizer: applied to genesio-tesi chaotic system. Nonlinear Dyn. 107(3), 2327–2343 (2022)

    Article  Google Scholar 

  5. Aslmostafa, E., Ghaemi, S., Mirzaei, M.J., Badamchizadeh, M.A., Ghiasi, A.R.: Fuzzy adaptive sliding mode controller for a chaotic system with uncertainties and disturbances. In: 2020 6th Iranian Conference on Signal Processing and Intelligent Systems (ICSPIS), pp. 1–5. IEEE (2020)

  6. Cui, R., Zhang, X., Cui, D.: Adaptive sliding-mode attitude control for autonomous underwater vehicles with input nonlinearities. Ocean Eng. 123, 45–54 (2016)

    Article  Google Scholar 

  7. Li, J., Yang, Y., Hua, C., Guan, X.: Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode. IET Control Theory Appl. 11(8), 1184–1193 (2017)

    Article  MathSciNet  Google Scholar 

  8. Asadollahi, M., Ghiasi, A.R., Badamchizadeh, M.A.: Adaptive synchronization of chaotic systems with hysteresis quantizer input. ISA Trans. 98, 137–148 (2020)

    Article  Google Scholar 

  9. Zhong, C., Guo, Y., Yu, Z., Wang, L., Chen, Q.: Finite-time attitude control for flexible spacecraft with unknown bounded disturbance. Trans. Inst. Meas. Control 38(2), 240–249 (2016)

    Article  Google Scholar 

  10. Chen, W.H., Yang, J., Guo, L., Li, S.: Disturbance-observer-based control and related methods-an overview. IEEE Trans. Ind. Electron. 63(2), 1083–1095 (2015)

    Article  Google Scholar 

  11. Li, S., Yang, J., Chen, W.H., Chen, X.: Disturbance Observer-based Control: Methods and Applications. CRC Press (2014)

  12. Rabiee, H., Ataei, M., Ekramian, M.: Continuous nonsingular terminal sliding mode control based on adaptive sliding mode disturbance observer for uncertain nonlinear systems. Automatica 109, 108515 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mirzaei, M.J., Mirzaei, M., Aslmostafa, E., Asadollahi, M.: Robust observer-based stabilizer for perturbed nonlinear complex financial systems with market confidence and ethics risks by finite-time integral sliding mode control. Nonlinear Dyn. 105(3), 2283–2297 (2021)

    Article  Google Scholar 

  14. Chen, M., Chen, W.H.: Sliding mode control for a class of uncertain nonlinear system based on disturbance observer. Int. J. Adapt. Control Signal Process. 24(1), 51–64 (2010)

    MathSciNet  MATH  Google Scholar 

  15. Li, S., Sun, H., Yang, J., Yu, X.: Continuous finite-time output regulation for disturbed systems under mismatching condition. IEEE Trans. Automa. Control 60(1), 277–282 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mirzaei, M.J., Aslmostafa, E., Asadollahi, M., Badamchizadeh, M.A.: Robust adaptive finite-time stabilization control for a class of nonlinear switched systems based on finite-time disturbance observer. J. Frankl. Inst. 358(7), 3332–3352 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  17. Aslmostafa, E., Mirzaei, M.J., Asadollahi, M., Badamchizadeh, M.A.: Synchronization problem for a class of multi-input multi-output systems with terminal sliding mode control based on finite-time disturbance observer: Application to chameleon chaotic system. Chaos Solitons Fractals 150, 111191 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  18. Aslmostafa, E., Ghaemi, S., Badamchizadeh, M.A., Ghiasi, A.R.: Adaptive backstepping quantized control for a class of unknown nonlinear systems. ISA Trans. 125, 146–155 (2022)

    Article  Google Scholar 

  19. Aslmostafa, E., Mirzaei, M., Asadollahi, M., Badamchizadeh, M.: Free-will arbitrary time stabilisation problem for a class of nonlinear strict-feedback systems based on the backstepping method. Int. J. Control 1–13 (2022)

  20. Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design. John Wiley & Sons Inc (1995)

  21. Zhou, J., Wen, C., Wang, W., Yang, F.: Adaptive backstepping control of nonlinear uncertain systems with quantized states. IEEE Trans. Autom. Control 64(11), 4756–4763 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yu, J., Shi, P., Zhao, L.: Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica 92, 173–180 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  23. Farrell, J.A., Polycarpou, M., Sharma, M., Dong, W.: Command filtered backstepping. IEEE Trans. Autom. Control 54(6), 1391–1395 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ma, J., Park, J.H., Xu, S.: Command-filter-based finite-time adaptive control for nonlinear systems with quantized input. IEEE Trans. Autom. Control 66(5), 2339–2344 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ma, J., Zheng, Z., Li, P.: Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation. IEEE Trans. Cybern. 45(4), 728–741 (2014)

    Article  Google Scholar 

  26. Hou, Y., Tong, S.: Command filter-based adaptive fuzzy backstepping control for a class of switched nonlinear systems. Fuzzy Sets Syst. 314, 46–60 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yu, J., Shi, P., Dong, W., Yu, H.: Observer and command-filter-based adaptive fuzzy output feedback control of uncertain nonlinear systems. IEEE Trans. Ind. Electr. 62(9), 5962–5970 (2015)

    Article  Google Scholar 

  28. Qiao, L., Zhang, W.: Adaptive non-singular integral terminal sliding mode tracking control for autonomous underwater vehicles. IET Control Theory Appl. 11(8), 1293–1306 (2017)

    Article  MathSciNet  Google Scholar 

  29. Mobayen, S.: Design of novel adaptive sliding mode controller for perturbed chameleon hidden chaotic flow. Nonlinear Dyn. 92(4), 1539–1553 (2018)

    Article  MATH  Google Scholar 

  30. Yang, J., Li, S., Yu, X.: Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans. Ind. Electr. 60(1), 160–169 (2012)

    Article  Google Scholar 

  31. Shao, K., Zheng, J., Wang, H., Xu, F., Wang, X., Liang, B.: Recursive sliding mode control with adaptive disturbance observer for a linear motor positioner. Mech. Syst. Signal Process. 146, 107014 (2021)

    Article  Google Scholar 

  32. Bhat, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Control Signals Syst. 17(2), 101–127 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  33. Feng, Y., Han, F., Yu, X.: Chattering free full-order sliding-mode control. Automatica 50(4), 1310–1314 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  34. Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  35. Levant, A.: Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control 76(9–10), 924–941 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  36. Ursu, I., Ursu, F.: Active and Semiactive Control. Romanian Academy Publishing House, Bucharest (2002) (in Romanian).

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

    Ehsan Aslmostafa, Mostafa Asadollahi, Hamed Kharrati & Mohammad Javad Mirzaei

  2. Department of Mechanical, Automotive and Materials Engineering, University of Windsor, Windsor, Ontario, N9B 3P4, Canada

    Hamed Kharrati & Afshin Rahimi

Authors
  1. Ehsan Aslmostafa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mostafa Asadollahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hamed Kharrati
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Afshin Rahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mohammad Javad Mirzaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

EA: Conceptualization, methodology, software, writing-reviewing and editing, MJM: Conceptualization, methodology and software, MA: Conceptualization and project administration, HK and AR: Supervision, methodology and writing-reviewing & editing.

Corresponding author

Correspondence to Hamed Kharrati.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Code availability

Data will be made available on reasonable request.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (rar 100 KB)

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

Aslmostafa, E., Asadollahi, M., Kharrati, H. et al. Command-filtered-based technique for a class of nonlinear systems with finite-time observer in the presence of mismatched disturbances. Nonlinear Dyn 111, 10217–10228 (2023). https://doi.org/10.1007/s11071-023-08386-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08386-x

Keywords

Search

Navigation