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Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances

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Abstract

The problem of designing a sliding-mode controller for a class of fractional-order uncertain linear perturbed systems with Caputo derivative is addressed in this paper. Sufficient conditions for the existence of sliding surfaces guaranteeing the asymptotic stability of the reduced-order sliding-mode dynamics are obtained in terms of linear matrix inequalities, based on which and stability theory of fractional-order nonlinear systems; the corresponding reaching motion controller is proposed, and the reaching time is also obtained. Moreover, the upper bounds of the nonlinear uncertainties are not required to be known in advance, which can be tuned by the designed adaptive law. Meanwhile, some problems for the sliding-mode controller for fractional-order systems in existing literatures are pointed out. A numerical example is presented to demonstrate the validity and feasibility of the obtained results.

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Acknowledgments

The authors thank the referees and the editor for their valuable comments and suggestions. This work was supported by the National Natural Science Funds of China for Distinguished Young Scholar under Grant (No. 50925727), the National Natural Science Funds of China (Nos. 61403115, 61374135), the National Defense Advanced Research Project Grant (No. C1120110004), the Key Grant Project of Chinese Ministry of Education under Grant (No. 313018.) and the 211 project of Anhui University (No. KJJQ1102).

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China

    Liping Chen & Yigang He

  2. School of Mathematics, Anhui University, Hefei, 230039, China

    Ranchao Wu

  3. School of Automation, Chongqing University, Chongqing, 400044, China

    Yi Chai

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  1. Liping Chen
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  2. Ranchao Wu
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  3. Yigang He
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Correspondence to Liping Chen.

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Chen, L., Wu, R., He, Y. et al. Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances. Nonlinear Dyn 80, 51–58 (2015). https://doi.org/10.1007/s11071-014-1850-y

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  • DOI: https://doi.org/10.1007/s11071-014-1850-y

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