Skip to main content
SpringerLink
Log in

Observer-based adaptive control and faults estimation for T-S fuzzy singular fractional order systems

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper handles the issue of adaptive control and faults estimation of a class of T-S singular fractional order systems(SFOSs) with \(H_{\infty }\) performance, where the fractional order belongs to (0, 1). Firstly, a novel observer for SFOSs is proposed, which estimate unmeasurable or partially measurable state and faults, simultaneously. Secondly, regarding to the information obtained by the above observer and the designed adaptive parameters, an adaptive controller is proposed to estimate actuator faults of the SFOSs. Further, it is indispensable to ensure the admissibility of the proposed fuzzy SFOSs with \(H_{\infty }\) performance, novel sufficient conditions are obtained by linear matrix inequalities (LMIs), Finally, to illustrate the method proposed above is available, simulation examples are presented.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Cai L, Thornhill F, Pal C (2017) Multivariate detection of power system disturbances based on fourth order moment and singular value decomposition. IEEE Trans Power Syst 32(6):4289–4297

    Article  Google Scholar 

  2. Li L, Zhang Q, Zhu B (2015) Fuzzy stochastic optimal guaranteed cost control of bio-economic singular markovian jump systems. IEEE Trans Cybern 45(11):2512–2521

    Article  Google Scholar 

  3. Wang Y, Xia Y, Shen H, Zhou P (2018) SMC design for robust stabilization of nonlinear markovian jump singular systems. IEEE Trans Autom Control 63(1):219–224

    Article  MathSciNet  Google Scholar 

  4. Liang S, Wei Y, Pan J, Wang Y (2015) Bounded real lemmas for fractional order systems. Int J Autom Comput 12(2):192–198

    Article  Google Scholar 

  5. Shen H, Men Y, Wu Z, Park JH (2018) Nonfragile \(\cal{H}_{\infty }\) control for fuzzy markovian jump systems under fast sampling singular perturbation. IEEE Trans Syst Man Cybern Syst 48(12):2058–2069

    Article  Google Scholar 

  6. Xiao X, Park J, Zhou L, Lu G (2019) New results on stability analysis of Markovian switching singular systems. IEEE Trans Autom Control 64(5):2084–2091

    Article  MathSciNet  Google Scholar 

  7. Wei Y, Wang J, Liu T, Wang Y (2019) Sufficient and necessary conditions for stabilizing singular fractional order systems with partically measurable state. J Franklin Inst 356(4):1975–1990

    Article  MathSciNet  Google Scholar 

  8. Liu H, Pan Y, Li S, Chen Y (2017) Adaptive fuzzy backstepping control of fractional-order nonlinear systems. IEEE Trans Syst Man Cybern Syst 47(8):2209–2217

    Article  Google Scholar 

  9. Zhang X, Huang W, Wang Q (2021) Robust \(H_{\infty }\) adaptive sliding mode fault tolerant control for T-S fuzzy fractional order systems with mismatched disturbances. IEEE Trans Circuits Syst I Regul Papers. https://doi.org/10.1109/TCSI.2020.3039850

    Article  MathSciNet  Google Scholar 

  10. Sabatier J, Moze M, Farges C (2010) LMI stability conditions for fractional order systems. Comput Math Appl 59(5):1594–1609

    Article  MathSciNet  Google Scholar 

  11. Lu J, Chen Y (2010) Robust stability and stabilization of fractional-order interval systems with the fractional order \(\alpha \): the \( 0 < \alpha < 1\) case. IEEE Trans Autom Control 55(1):152–158

  12. Song S, Zhang B, Xia J, Zhang Z (2020) Adaptive backstepping hybrid fuzzy sliding mode control for uncertain fractional-order nonlinear systems based on finite-time scheme. IEEE Trans Syst Man Cybern Syst 50(4):1559–1569

    Article  Google Scholar 

  13. Pu Y, Yi Z, Zhou J (2017) Fractional Hopfield neural networks: fractional dynamic associative recurrent neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2319–2333

    Article  MathSciNet  Google Scholar 

  14. Guo Y, Lin C, Chen B, Wang QG (2018) Stablization for singular fractional order systems via static output feedback. IEEE Access 6:71678–71684

    Article  Google Scholar 

  15. Zhang X, Chen Y (2018) Admissibility and robust stabilization of continous linear singular fractional order systems with fractional order \(\alpha:\) the \(0{<}\alpha {<}1\) case. ISA Trans 82(4):42–50

    Article  Google Scholar 

  16. Zhang Q, Qiao L, Zhu B, Zhang H (2017) Dissipativity analysis and synthesis for a class of T-S fuzzy descriptor systems. IEEE Trans Syst Man Cybern Syst 47(8):1774–1784

    Article  Google Scholar 

  17. Wang L, Lam H-K (2020) Further study on observer design for continuous-time Takagi-Sugeno fuzzy model with unknown premise variables via average dwell time. IEEE Trans Cybern 50(11):4855–4860. https://doi.org/10.1109/TCYB.2019.2933696

    Article  Google Scholar 

  18. Han J, Zhang H, Wang Y, Liu X (2016) Robust state/fault estimation and fault tolerant control for T-S fuzzy systems with sensor and actuator faults. J Franklin Inst 353(2):615–641

    Article  MathSciNet  Google Scholar 

  19. Su X, Shi P, Wu L, Song Y (2016) Fault detection filtering for nonlinear switched stochastic systems. IEEE Trans Autom Control 61(5):1310–1315

    Article  MathSciNet  Google Scholar 

  20. Zhang H, Qin C, Jiang B, Luo Y (2014) Online adaptive policy learning algorithm for \(h_{\infty }\) state feedback control of unknown affine nonlinear discrete-time systems. IEEE Trans Cybern 44(12):2706–2718

    Article  Google Scholar 

  21. Li R, Zhang X (2020) Adaptive sliding mode observer design for a class T-S descriptor fractional order system. IEEE Trans Fuzzy Syst 28(9)

  22. Asemani MH, Majd VJ (2013) A robust \(H_{\infty }\) observer-based controller design for uncertain T-S fuzzy systems with unknown premise variables via LMI. Fuzzy Sets Syst 212(1):21–40

    Article  MathSciNet  Google Scholar 

  23. Zhang H, Liu Y, Wang Y (2021) Observer-based finite-time adaptive fuzzy control for nontriangular nonlinear systems with full-state constraints. IEEE Trans Cybern 51(3):1110–1120. https://doi.org/10.1109/TCYB.2020.2984791

    Article  Google Scholar 

  24. Chen B, Lin C, Liu X, Liu K (2016) Observer-based adaptive fuzzy control for a class of nonlinear delayed systems. IEEE Trans Syst Man Cybern Syst 46(1):27–36

    Article  Google Scholar 

  25. Zhang H, Zhang J, Yang G, Luo Y (2015) Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming. IEEE Trans Fuzzy Syst 23(1):152–163

    Article  Google Scholar 

  26. Tahoun A, Arefa M (2020) A new unmatched-disturbances compensation and fault-tolerant control for partically known nonlinear singular systems. ISA Trans 104(31):310–320

    Article  Google Scholar 

  27. Zhang H, Liang Y, Su H, Liu C (2020) Event-driven guaranteed cost control design for nonlinear systems with actuator faults via reinforcement learning algorithm. IEEE Transactions on Systems, Man, and Cybernetics: Systems 50(11):4135–4150

    Article  Google Scholar 

  28. Li M, Liu M, Zhang Y (2020) Asynchronous adaptive dynamic output feedback sliding mode control for singular markovian jump systems with actuator faults and uncertain transition rates. Appl Math Comput. https://doi.org/10.1016/j.amc.2019.124958

    Article  MathSciNet  MATH  Google Scholar 

  29. Chen K, Astolfi A (2021) Adaptive control for systems with time-varying parameters. IEEE Trans Autom Control 66(5):1986–2001

    Article  MathSciNet  Google Scholar 

  30. Xu S, Lam J (2006) Roubust control and filering of singular systems. Springer-Verlag, Germany, Berlin

    Google Scholar 

  31. Li Y, Wei Y, Chen Y, Wang Y (2020) A universal framework of the generalized Kalman-Yakubovich-Popov Lemma for singular fractional-order systems. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2945358

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Box 134, 110819, Shenyang, People’s Republic of China

    Yuqing Yan, Zhongyang Ming & Yingchun Wang

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, 110004, China

    Huaguang Zhang

Authors
  1. Yuqing Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaguang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhongyang Ming
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yingchun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaguang Zhang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors. Informed consent was obtained from all individual.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, Y., Zhang, H., Ming, Z. et al. Observer-based adaptive control and faults estimation for T-S fuzzy singular fractional order systems. Neural Comput & Applic 34, 4265–4275 (2022). https://doi.org/10.1007/s00521-021-06527-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-06527-0

Keywords

Search

Navigation