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Robust tracking control design for fractional-order interval type-2 fuzzy systems

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Abstract

This paper is concerned with an uncertainty and disturbance estimator-based tracking control problem for a class of interval type-2 fractional-order Takagi-Sugeno fuzzy systems subject to time-varying delays. The footprints of the uncertainty of the underlying fuzzy systems are taken into account to capture and model different levels of uncertainties. The uncertainty and disturbance estimator is used to promote the tracking behavior of rejecting disturbance in the control system. First, by applying the Lyapunov approach, we focus on the examination of stability and performance of the fractional-order tracking error system. Next, unknown system uncertainties, external disturbances and nonlinearities are accurately estimated via an appropriate filter design. Particularly, the proposed control technique does not require any prior knowledge about above said unknown factors and it only requires the bandwidth information about the low-pass filter. Then, four numerical examples with simulation results are presented in the end, to show the potential of the theoretical results of the proposed control method.

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Acknowledgements

The work of first, third and fourth authors was supported in part 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 Grand Information Technology Research Center Support Program supervised by the Institute for Information & Communications Technology Planning & Evaluation (IITP) under Grant IITP-2021-2020-0-01462.

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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 & Palanisamy Selvaraj

  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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  4. Palanisamy Selvaraj
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Correspondence to Oh-Min Kwon.

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Kavikumar, R., Sakthivel, R., Kwon, OM. et al. Robust tracking control design for fractional-order interval type-2 fuzzy systems. Nonlinear Dyn 107, 3611–3628 (2022). https://doi.org/10.1007/s11071-021-07163-y

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