引用本文:王军义,张文涛,刘振伟,姜杨.基于仿射Bessel-Legendre不等式和不确定转移率的 神经网络稳定性[J].控制理论与应用,2022,39(1):41~47.[点击复制]
WANG Jun-yi,ZHANG Wen-tao,LIU Zhen-wei,JIANG Yang.Stability for neural networks based on affine Bessel-Legendre inequality and uncertain transition rates[J].Control Theory and Technology,2022,39(1):41~47.[点击复制]
基于仿射Bessel-Legendre不等式和不确定转移率的 神经网络稳定性
Stability for neural networks based on affine Bessel-Legendre inequality and uncertain transition rates
摘要点击 1602  全文点击 564  投稿时间：2020-11-26  修订日期：2021-05-17
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DOI编号  10.7641/CTA.2021.00841
  2022,39(1):41-47
中文关键词  马尔科夫神经网络系统  不确定转移率  仿射Bessel-Legendre(B-L)不等式  增广Lyapunov-Krasovskii泛函
英文关键词  Markovian neural networks system  uncertain transition rates  affine Bessel-Legendre (B-L) inequality  augmented Lyapunov-Krasovskii functional
基金项目  国家自然科学基金项目(61903075, U20A20197), 辽宁省自然科学基金项目(2019–KF–03–02, 2019–MS–116), 中央高校基本科研业务费项目 (N2026003, N2004014, N2126006), 教育部春晖计划合作科研项目(LN2019006), 辽宁省科技重大专项计划项目(2019JH1/10100005), 辽宁省重点 研发计划项目(2020JH2/10100040)资助.
作者单位E-mail
王军义* 东北大学机器人科学与工程学院 wjyi168@126.com 
张文涛 东北大学机器人科学与工程学院  
刘振伟 东北大学信息科学与工程学院  
姜杨 东北大学机器人科学与工程学院  
中文摘要
      针对具有时变时滞和不确定转移率的马尔科夫神经网络系统, 充分考虑马尔科夫转移率的不确定特性, 利 用基于松弛变量的有效技术代替传统不等式来约束转移速率中的不确定项, 从而减少了决策变量的个数并降低了 计算复杂度. 通过建立时滞依赖的增广Lyapunov-Krasovskii泛函, 并基于仿射Bessel-Legendre(B-L)不等式, 给出依 赖于时滞和时滞导数上下界的具有较小保守性的神经网络系统稳定条件. 最后, 通过两个数值例子说明了理论结果 的有效性.
英文摘要
      For Markovian neural network with time-varying delays and uncertain transition rates, the effective relaxation variable technique instead of the traditional inequality is adopted to restrain the uncertain terms of the transition rates by fully considering the uncertain characteristic of Markovian transition rates, which reduces the number of decision variables and the computational complexity. By applying the delayed-dependent augmented Lyapunov-Krasovskii functional, and affine Bessel-Legendre (B-L) inequality, the less conservative stability conditions that are dependent on upper and lower bounds of delay and delay derivative are proposed. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.