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Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control

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Abstract

This paper considers synchronization between two fractional-order neural networks (FONNs). To handle the case of full/under-actuation, i.e. the dimension of the synchronization controller is equal to or less than that of the FONNs, a novel fractional-order integral sliding surface is designed, and the feasibility of the proposed approach is shown by solving two linear matrix inequalities. Then, based on the fractional Lyapunov stability criterion, a fractional-order sliding mode controller equipped with fractional-order adaptation laws is constructed to guarantee the synchronization error converging to an arbitrary small region of the origin. The effectiveness of the proposed control method is verified by two simulation examples.

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Acknowledgements

The authors are indebted to the anonymous reviewers’ valuable comments, which improved the presentation and quality of this paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11401243, 61403157), the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (Grant No. KJ2015A256), the Fundamental Research Funds for the Central Universities of China (Grant No. GK201504002), the Foundation for Distinguished Young Talents in Higher Education of Anhui, China (Grant No. GXYQZD2016257), and the Innovation Funds of Graduate Programs of Shaanxi Normal University (Grant No. 2015CXB008).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Heng Liu, Shenggang Li & Ye Chen

  2. Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China

    Heng Liu

  3. Department of Biomedical Engineering, National University of Singapore, 117583, Singapore, Singapore

    Yongping Pan

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  1. Heng Liu
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Correspondence to Yongping Pan.

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Liu, H., Pan, Y., Li, S. et al. Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control. Int. J. Mach. Learn. & Cyber. 9, 1219–1232 (2018). https://doi.org/10.1007/s13042-017-0646-z

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