分数双向关联记忆神经网络的稳定性分析,具有多个比例延迟和分布式延迟
IEEE transactions on neural networks and learning systems
|December 13, 2023
概括
本研究为具有多次延迟的分数顺序双向关联记忆神经网络 (FOBAMNNs) 建立了有限时间稳定性标准. 对于FOBAMNNs,开发了新型Gronwall不平等,使得在较弱条件下进行分析.
科学领域:
- 神经网络的神经网络的神经网络
- 控制理论 控制理论
- 分数微积分的计算.
背景情况:
- 分数顺序双向联想记忆神经网络 (FOBAMNNs) 在复杂系统中至关重要.
- 通过多个比例和分布式延迟来分析它们的稳定性提出了重大挑战.
- 对于具有多个比例延迟和变化的分数顺序的系统,现有的Gronwall不等式是不够的.
研究的目的:
- 调查FOBAMNNs具有多个比例和分布式延迟的有限时间稳定性.
- 开发新的Gronwall积分不等式,适用于具有多个比例延迟的分数顺序系统.
- 在宽松的条件下推导出稳定性标准,超越全球利普希茨要求.
主要方法:
- 开发一个新的Gronwall积分不等式,用于分数计算中的多重比例延迟.
- 一般化的分数多比例延迟的构造"Gronwall不同级别的不等式.
- 应用这些不平等来确定FOBAMNN的有限时间稳定性标准.
主要成果:
- 首次确定了多个比例延迟的新型格伦沃尔积分不等式.
- 对于具有分数订单的FOBAMNNs,新的有限时间稳定性标准得到了推导.
- 由此产生的标准在较弱的条件下适用,包括线性增长约束.
结论:
- 提出的方法有效地分析了FOBAMNNs的有限时间稳定性,具有多次延迟.
- 新开发的不等式为分数顺序系统提供了更普遍的方法.
- 数字实验证实了衍生稳定性标准的有效性和有效性.
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