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Input-output finite-time IT2 fuzzy dynamic sliding mode control for fractional-order nonlinear systems

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Abstract

In this work, the issue of input-output finite-time stabilization of fractional-order nonlinear systems represented by interval type-2 fuzzy models is discussed. Specifically, the addressed system takes into account more realistic factors such as uncertainties, nonlinearities, disturbances, and state delays. A new dynamic sliding-mode control (SMC) scheme for interval type-2 fuzzy models is developed in order to eliminate the commonly held assumption that all subsystems share the same input matrix (i.e. \(B^i \ne B\)), which is considered in the majority of fuzzy SMC scheme results. Based on input-output finite-time stabilization properties and the proposed control scheme, the goal of this work is to reduce the impact of uncertainties, nonlinearities, disturbances, and state delays while ensuring that the signal variables arrive at a domain within the designed fixed-time level. Furthermore, the required criteria are expressed as linear matrix inequalities, which can be solved by using MATLAB linear matrix inequality toolbox. Following that, three numerical examples, including the permanent magnet synchronous motor model and the single-link robot arm model, are provided to validate the proposed control scheme.

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References

  1. Chen, L., Wu, R., Cheng, Y., Chen, Y., Zhuang, C.: Delay-dependent and order-dependent stability and stabilization of fractional-order linear systems with time-varying delay. IEEE Trans. Circuits Syst. II Reg. Papers. 67(3), 1064–1068 (2020)

  2. Chen, L., Li, T., Wu, R., Chen, Y.Q., Liu, Z.: Non-fragile control for a class of fractional-order uncertain linear systems with time-delay. IET Control Theory Appl. 14(12), 1575–1589 (2020)

    Article  MathSciNet  Google Scholar 

  3. Chen, L., Wu, R., He, H., Chai, Y.: Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances. Nonlinear Dyn. 80, 51–58 (2015)

    Article  MathSciNet  Google Scholar 

  4. Hu, T., He, Z., Zhang, X., Zhong, S.: Leader-following consensus of fractional-order multi-agent systems based on event-triggered control. Nonlinear Dyn. 99, 2219–2232 (2020)

    Article  Google Scholar 

  5. Podlubny, I.: Fractional differential equations. Academic Press, New York (1999)

    MATH  Google Scholar 

  6. Zou, C.F., Hu, X.S., Dey, S., Zhang, L., Tang, X.: Nonlinear fractional-order estimator with guaranteed robustness and stability for lithium-ion batteries. IEEE Trans. Ind. Electron. 65(7), 5951–5961 (2018)

    Google Scholar 

  7. Islam, S.I., Lim, C.C., Shi, P.: Robust fault detection of T-S fuzzy systems with time-delay using fuzzy functional observer. Fuzzy Sets Syst. 392, 1–23 (2020)

    Article  MathSciNet  Google Scholar 

  8. Shen, H., Xing, M., Wu, Z.G., Park, Ju.H.: Fault-tolerant control for fuzzy switched singular systems with persistent dwell-time subject to actuator fault. Fuzzy Sets Syst. 392, 60–76 (2020)

    Article  MathSciNet  Google Scholar 

  9. Wang, L., Lam, H.K.: \(H_\infty \) control for continuous-time Takagi-Sugeno fuzzy model by applying generalized Lyapunov function and introducing outer variables. Automatica. 125, 109409 (2021)

    Article  MathSciNet  Google Scholar 

  10. Wang, X., Park, Ju.H., Yang, H., Zhao, G., Zhong, S.: An improved fuzzy sampled-data control to stabilization of T-S fuzzy systems with state delays. IEEE Trans. Cybern. 50(7), 3125–3135 (2019)

    Article  Google Scholar 

  11. Zhang, L., Yang, G.H.: Observer-based fuzzy adaptive sensor fault compensation for uncertain nonlinear strict-feedback systems. IEEE Trans. Fuzzy Syst. 26(4), 2301–2310 (2018)

    Article  Google Scholar 

  12. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)

    Article  Google Scholar 

  13. Lam, H.K., Seneviratne, L.D.: Stability analysis of interval type-2 fuzzy-model-based control systems. IEEE Trans. Syst. Man Cybern. B, Cybern 38(3), 617–628 (2008)

    Article  Google Scholar 

  14. Wu, D., Mendel, J.M.: On the continuity of type-1 and interval type-2 Fuzzy logic systems. IEEE Trans. Fuzzy Syst. 19, 179–192 (2011)

    Article  Google Scholar 

  15. Du, Z., Kao, Y., Park, Ju.H.: Interval type-2 fuzzy sampled data control of time delay systems. Inform. Sci. 487, 193–207 (2019)

    Article  MathSciNet  Google Scholar 

  16. Shanmugam, L., Joo, Y.H.: Design of interval type-2 fuzzy-based sampled-data controller for nonlinear systems using novel fuzzy Lyapunov functional and its application to PMSM. IEEE Trans. Syst. Man Cybern. Syst. 51(1), 1297–1307 (2021)

    Article  Google Scholar 

  17. Lian, Z., Shi, P., Lim, C.C.: Hybrid-triggered interval type-2 fuzzy control for networked systems under attacks. Inform. Sci. 567, 332–347 (2021)

    Article  MathSciNet  Google Scholar 

  18. Xiao, B., Lam, H.K., Yu, Y., Li, Y.: Sampled-data output-feedback tracking control for interval type-2 polynomial fuzzy systems. IEEE Trans. Fuzzy Syst. 28(3), 424–433 (2020)

    Article  Google Scholar 

  19. 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. 29(4), 927–939 (2021)

    Article  Google Scholar 

  20. Li, Y., Li, J.: Stability analysis of fractional order systems based on T-S fuzzy model with the fractional order \(\alpha \) : 0 \(<\alpha <1\). Nonlinear Dyn. 78(4), 2909–2919 (2014)

  21. Mirzajani, S., Aghababa, M.P., Heydari, A.: Adaptive T-S fuzzy control design for fractional-order systems with parametric uncertainty and input constraint. Fuzzy Sets Syst. 365, 22–39 (2019)

    Article  MathSciNet  Google Scholar 

  22. Zhang, X., Huang, W.: Robust \(H_\infty \) adaptive output feedback sliding mode control for interval type-2 fuzzy fractional-order systems with actuator faults. Nonlinear Dyn. 104, 537–550 (2021)

    Article  Google Scholar 

  23. Zhang, X., Huang, W., Wang, Q.G.: Robust \(H_\infty \) adaptive sliding mode fault tolerant control forT-S fuzzy fractional-order systems with mismatched disturbances. IEEE Trans. Circuits Syst. I Reg. Papers 68(3), 1297–1307 (2021)

    Article  Google Scholar 

  24. Jing, B., Karimi, H.R., Kao, Y., Gao, C.: Takagi-Sugeno model based event-triggered fuzzy sliding-mode control of networked control systems with semi-Markovian switchings. IEEE Trans. Fuzzy Syst. 28(4), 673–683 (2020)

    Article  Google Scholar 

  25. Li, H.Y., Wang, J.H., Shi, P.: Output-feedback based sliding mode control for fuzzy systems with actuator saturation. IEEE Trans. Fuzzy Syst. 24(6), 1282–1293 (2016)

    Article  Google Scholar 

  26. Qi, W., Yang, X., Park, Ju.H., Cao, J., Cheng, J.: Fuzzy SMC for quantized nonlinear stochastic switching systems with semi-Markovian process and application. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3069423

    Article  Google Scholar 

  27. Xue, Y., Zheng, B.C., Yu, X.: Robust sliding mode control for T-S fuzzy systems via quantized state feedback. IEEE Trans. Fuzzy Syst. 28(4), 2261–2272 (2018)

    Article  Google Scholar 

  28. Gao, Q., Feng, G., Xi, Z., Wang, Y., Qiu, J.: Robust \(H_\infty \) control of T-S fuzzy time-delay systems via a new sliding-mode control scheme. IEEE Trans. Fuzzy Syst. 22(2), 459–465 (2014)

    Article  Google Scholar 

  29. Gao, Q., Feng, G., Xi, Z., Wang, Y., Qiu, J.: A new design of robust \(H_\infty \) sliding mode control for uncertain stochastic T-S fuzzy time-delay systems. IEEE Trans. Fuzzy Syst. 44(9), 1556–1566 (2014)

  30. Ji, W., Qiu, J., Wu, L., Lam, H.K.: Fuzzy-affine-model-based output feedback dynamic sliding mode controller design of nonlinear systems. IEEE Trans. Fuzzy Syst. 51(3), 1652–1661 (2021)

  31. Wen, S., Chen, Z.Q., Zeng, Z., Yu, X., Huang, T.: Fuzzy control for uncertain vehicle active suspension systems via dynamic sliding-mode approach. IEEE Trans. Syst. Man Cybern. 47(1), 24–32 (2017)

    Article  Google Scholar 

  32. Wei, Y., Karimi, H.R.: Dynamic sliding mode control for nonlinear parameter-varying systems. Int. J. Robust Nonlinear Control. 1–21 (2021)

  33. Delavari, H., Ghaderi, R., Ranjbar, A., Momani, S.: Fuzzy fractional order sliding mode controller for nonlinear systems. Commun. Nonlinear Sci. Numerical Simul. 15(4), 963–978 (2010)

    Article  MathSciNet  Google Scholar 

  34. Dorato, P.: Short time stability in linear time-varying systems. in Proc. IRE Int. Convention Rec. 83–87(1961)

  35. Amato, F., Ambrosino, R., Cosentino, C., Tommasi, G.D.: Input-output finite time stabilization of linear systems. Automatica. 46(9), 1558–1562 (2010)

    Article  MathSciNet  Google Scholar 

  36. Chen, M., Sun, J.: Input-output finite-time reliable static output control of time-varying system with input delay. IEEE Trans. Syst. Man Cybern. 51(2), 1334–1344 (2021)

    Article  Google Scholar 

  37. Qi, W., Yang, X., Ahn, C.K., Cao, J., Cheng, J.: Input-output finite-time sliding-mode control for T-S fuzzy systems with application. IEEE Trans. Syst. Man Cybern. (2020). https://doi.org/10.1109/TSMC.2019.2954854

    Article  Google Scholar 

  38. Ren, H., Zong, G., Li, T.: Event-triggered finite-time control for networked switched linear systems with asynchronous switching. IEEE Trans. Syst. Man Cybern. 48(11), 1874–1884 (2018)

    Article  Google Scholar 

  39. Ren, H., Zong, G., Ahn, C.K.: Event-triggered finite-time resilient control for switched systems: an observer-based approach and its applications to a boost converter circuit system model. Nonlinear Dyn. 94, 2409–2421 (2018)

    Article  Google Scholar 

  40. Wang, K., Tian, E., Shen, S., Wei, L., Zhang, J.: Input-output finite-time stability for networked control systems with memory event-triggered scheme. J. Frankl. Inst. 356, 8507–8520 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1A6A1A12047945) and in part by the MSIT (Ministry of Science and ICT), Korea, under the Grand Information Technology Research Center support program (IITP-2022-2020-0-01462) supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation).

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Authors and Affiliations

  1. School of Electrical Engineering, Chungbuk National University, 1 Chungdae-ro, Cheongju, 28644, South Korea

    Ramasamy Kavikumar, Oh-Min Kwon & Seung-Hoon Lee

  2. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India

    Rathinasamy Sakthivel

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea

    Rathinasamy Sakthivel

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  1. Ramasamy Kavikumar
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  2. Oh-Min Kwon
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  3. Seung-Hoon Lee
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  4. Rathinasamy Sakthivel
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Correspondence to Oh-Min Kwon or Rathinasamy Sakthivel.

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Kavikumar, R., Kwon, OM., Lee, SH. et al. Input-output finite-time IT2 fuzzy dynamic sliding mode control for fractional-order nonlinear systems. Nonlinear Dyn 108, 3745–3760 (2022). https://doi.org/10.1007/s11071-022-07442-2

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