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Asymptotic pseudo-state stabilization of commensurate fractional-order nonlinear systems with additive disturbance

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Abstract

The pseudo-state stabilization problem of commensurate fractional-order nonlinear systems is investigated. The concerned fractional-order nonlinear system is of parametric strict-feedback form with both unknown parameters and the additive disturbance. To solve this problem, a new nonlinear adaptive control law is constructed via fractional-order backstepping scheme. The developed fractional-order controller does not require the knowledge about both the interval of uncertain parameters and the upper bound of the additive disturbance. The asymptotic pseudo-state stability of the closed-loop system is proved in terms of fractional Lyapunov stability. Several examples are performed finally, and the efficiency is verified.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61171034, the Fundamental Research Funds for the Central Universities and the Province Natural Science Fund of Zhejiang under Grant R1110443.

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Authors and Affiliations

  1. College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China

    Dongsheng Ding, Donglian Qi & Qiao Wang

  2. CSR Zhuzhou Electric Locomotive CO., LTD, Zhuzhou, 412001, China

    Junmin Peng

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  1. Dongsheng Ding
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  2. Donglian Qi
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  3. Junmin Peng
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  4. Qiao Wang
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Correspondence to Dongsheng Ding.

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Ding, D., Qi, D., Peng, J. et al. Asymptotic pseudo-state stabilization of commensurate fractional-order nonlinear systems with additive disturbance. Nonlinear Dyn 81, 667–677 (2015). https://doi.org/10.1007/s11071-015-2018-0

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