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Adaptive control for discontinuous variable-order fractional systems with disturbances

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Abstract

This paper deals with the global asymptotic stabilization and finite-time stabilization issues for variable-order fractional systems with partial a priori bounded disturbances by designing an appropriate adaptive controller. Via the inductive method and Arzela-Ascoli theorem, the existence and uniqueness of the solution for the considered system is firstly verified under the proposed control strategy. By applying Lyapunov stability theory, non-smooth analysis and inequality technique, sufficient stabilization criteria are established under the framework of variable-order fractional Filippov differential inclusion. Finally, two numerical simulations are given to demonstrate the validity of the proposed method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China Nos. 61773281, 61673292, 61933014.

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Authors and Affiliations

  1. Tianjin Key Laboratory of Process Measurement and Control, School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, People’s Republic of China

    Xiao Peng, Yijing Wang & Zhiqiang Zuo

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  1. Xiao Peng
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  2. Yijing Wang
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  3. Zhiqiang Zuo
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Correspondence to Zhiqiang Zuo.

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Peng, X., Wang, Y. & Zuo, Z. Adaptive control for discontinuous variable-order fractional systems with disturbances. Nonlinear Dyn 103, 1693–1708 (2021). https://doi.org/10.1007/s11071-021-06199-4

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