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G−布朗运动驱动的时滞神经网络的稳定性分析

丁畅 沈波

丁畅, 沈波. G−布朗运动驱动的时滞神经网络的稳定性分析[J]. 上海工程技术大学学报, 2022, 36(2): 130-138. doi: 10.12299/jsues.22-0014
引用本文: 丁畅, 沈波. G−布朗运动驱动的时滞神经网络的稳定性分析[J]. 上海工程技术大学学报, 2022, 36(2): 130-138. doi: 10.12299/jsues.22-0014
DING Chang, SHEN Bo. Stability analysis for time-delayed neural networks driven by G−Brownian motion[J]. Journal of Shanghai University of Engineering Science, 2022, 36(2): 130-138. doi: 10.12299/jsues.22-0014
Citation: DING Chang, SHEN Bo. Stability analysis for time-delayed neural networks driven by G−Brownian motion[J]. Journal of Shanghai University of Engineering Science, 2022, 36(2): 130-138. doi: 10.12299/jsues.22-0014

G−布朗运动驱动的时滞神经网络的稳定性分析

doi: 10.12299/jsues.22-0014
基金项目: 国家自然科学基金面上项目资助(61873059)
详细信息
    作者简介:

    丁畅:丁 畅(1996−),男,在读硕士,研究方向为随机非线性控制. E-mail:2191728@mail.dhu.edu.cn

    通讯作者:

    沈 波(1981−),男,教授,博士,研究方向为随机非线性控制. E-mail:bo.shen@dhu.edu.cn

  • 中图分类号: O231.3

Stability analysis for time-delayed neural networks driven by G−Brownian motion

  • 摘要:

    研究一类由G−布朗运动驱动的时滞神经网络(G−DNN)的稳定性问题. 实际中噪声并不总是服从正态分布,为更好地描述实际情形,采用G−布朗运动来描述噪声,分析G−布朗运动噪声的离散观测值对时滞神经网络稳定性的影响. 针对指数稳定的时滞神经网络,引入由G−布朗运动驱动的随机噪声,并利用G−随机分析理论、Gronwall不等式、Borel-Cantelli引理等,给出随机噪声强度的上界,使得在噪声强度少于该上界的情形下随机时滞递归神经网络的稳定速度大于原来神经网络的稳定速度. 进一步分析噪声在离散的情形下随机时滞递归神经网络的稳定性问题. 借助G−Itô公式、放缩技巧及一些基本不等式,得到能进一步加快随机时滞递归神经网络指数稳定速度的噪声离散步长的上界. 通过实例验证了理论结果的有效性.

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出版历程
  • 收稿日期:  2022-01-21
  • 录用日期:  2022-01-21
  • 网络出版日期:  2022-11-16
  • 刊出日期:  2022-06-30

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