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Finite-Time Robust Synchronization of Memrisive Neural Network with Perturbation

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Abstract

In this paper, we study finite-time synchronization of a memristive neural network (MNN) with impulsive effect and stochastic perturbation. Because the parameters of the MNN are state-dependent, the traditional analytical method and control technique can not be directly used. In previous research, differential inclusions theory and set-valued mappings technique have been recently introduced to deal with this MNN system. But, we study the synchronization of MNN without using the previous solution technique. A novel analytical technique is first proposed to transform the MNN to a class of neural network (cNN) with uncertain parameters. The finite-time synchronization is obtained by disposing of parameter mismatch, impulsive effect or stochastic perturbation for the cNN. Several useful criteria of synchronization are obtained based on Lyapunov function, linear matrix inequality (LMI) and finite-time stability theory. Finally, two examples are given to demonstrate the effectiveness of our proposed method.

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Acknowledgements

The authors thank all the Editor and the anonymous referees for their constructive comments and valuable suggestions, which are helpful to improve the quality of this paper. The work is supported by the National Key Research and Development Program (Grant Nos. 2016YFB0800602, 2016YFB0800604) and the National Natural Science Foundation of China (Grant Nos. 61472045, 61573067).

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Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan, 250022, China

    Hui Zhao

  2. State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Hui Zhao & Jinghua Xiao

  3. State Key Laboratory of Public Big Data, Guizhou, 550025, China

    Yixian Yang

  4. State Key Laboratory of Networking and Switching Technology, Information Security Center, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing, 100876, China

    Lixiang Li, Haipeng Peng & Yixian Yang

  5. The National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Lixiang Li, Haipeng Peng & Yixian Yang

  6. Potsdam Institute for Climate Impact Research, 14473, Potsdam, Germany

    Jürgen Kurths

Authors
  1. Hui Zhao
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  2. Lixiang Li
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  3. Haipeng Peng
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  4. Jürgen Kurths
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  5. Jinghua Xiao
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  6. Yixian Yang
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Correspondence to Lixiang Li.

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Zhao, H., Li, L., Peng, H. et al. Finite-Time Robust Synchronization of Memrisive Neural Network with Perturbation. Neural Process Lett 47, 509–533 (2018). https://doi.org/10.1007/s11063-017-9664-9

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  • DOI: https://doi.org/10.1007/s11063-017-9664-9

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