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Adaptive chaos control of the fractional-order arch MEMS resonator

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Abstract

This paper addresses adaptive chaos control issue for the fractional-order arch MEMS resonator with fully unknown function, chaotic vibration and time delay under distributed electrostatic actuation. The phase diagrams and time histories are presented to investigate characteristic of chaotic attractor for the fractional-order arch MEMS resonator. In the process of controller design, the Chebyshev neural network with a weight and fractional-order adaptive law is employed to approximate complicated unknown function. In view of more advantages in modeling the behavior of the arch MEMS resonator in contrast to integer-order calculus, the fractional-order adaptive chaos control technology by merging Chebyshev neural network and backstepping is presented to guarantee the stability based on the fractional-order Lyapunov stability criterion. Finally, simulation studies are presented to illustrate feasibility of the proposed scheme.

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Acknowledgements

This work is funded by the National Natural Science Foundation of China (Nos. 51505170, 51475097, 51375506), National Smart Manufacturing Project (No. [2016]213), National Science-technology Support Plan Project (No. 2012BAF12B14) and Major Project of Basic Research of Guizhou Province (No. [2014]2001).

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, 550025, China

    Shaohua Luo & Shaobo Li

  2. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Shaobo Li

  3. Department of Mechanical Engineering, Erik Jonsson School of Engineering and Computer Science, The University of Texas at Dallas, Richardson, TX, 75080, USA

    Farid Tajaddodianfar

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  1. Shaohua Luo
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  2. Shaobo Li
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  3. Farid Tajaddodianfar
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Correspondence to Shaohua Luo.

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Luo, S., Li, S. & Tajaddodianfar, F. Adaptive chaos control of the fractional-order arch MEMS resonator. Nonlinear Dyn 91, 539–547 (2018). https://doi.org/10.1007/s11071-017-3890-6

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