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Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay

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Abstract

Based on the framework of Filippov solutions, this paper considers synchronization of inertial neural networks (INNs) with discontinuous activation functions and proportional delay. By designing several non-chattering controllers, both finite-time and fixed-time synchronization are studied. The designed controllers are simple to be implemented and can overcome the effects of both nonidentical uncertainties of Filippov solutions and the proportional delay without inducing any chattering. By designing new Lyapunov functionals and utilizing 1-norm methods, several sufficient conditions are obtained to ensure that the INNs achieve drive-response synchronization in finite time and fixed time, respectively. Moreover, the settling time is estimated for the two types of synchronization. Simulations are provided to illustrate the effectiveness of theoretical analysis.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61673078, 61463002, the Basic and Frontier Research Project of Chongqing under Grant No. cstc2018jcyjAX0369, and the Bowang Scholar of Chongqing Normal University.

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Authors and Affiliations

  1. School of Electrical Engineering, Liupanshui Normal University, Liupanshui, 553000, China

    Dengguo Xu

  2. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Dengguo Xu

  3. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Xinsong Yang & Rongqiang Tang

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  1. Dengguo Xu
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  2. Xinsong Yang
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  3. Rongqiang Tang
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Correspondence to Xinsong Yang.

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Xu, D., Yang, X. & Tang, R. Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay. Neural Process Lett 51, 2337–2353 (2020). https://doi.org/10.1007/s11063-020-10199-7

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