对于分数顺序延迟神经网络的几乎周期性解决方案的多重Mittag-Leffler稳定性:分布式优化方法
IEEE transactions on neural networks and learning systems
|November 10, 2023
概括
这项研究引入了关于分数顺序延迟神经网络 (FDNNs) 多重Mittag-Leffler稳定性的新理论. 分布式优化方法用于管理复杂的条件,提高计算效率.
科学领域:
- 动态系统和控制理论.
- 计算神经科学是一种神经科学.
- 非线性分析 非线性分析
背景情况:
- 分数顺序延迟神经网络 (FDNNs) 呈现出复杂的动态.
- 了解FDNN中几乎周期性解决方案 (APO) 的稳定性至关重要.
- 分析高维NN稳定性的现有方法可能是计算密集的.
研究的目的:
- 研究 APO 在具有非线性,非单调激活函数的 FDNN 中的多个 Mittag-Leffler 稳定性.
- 开发一种方法来解决相关的代数不等式条件,特别是对于高维系统.
- 为传统方法提供计算效率高的替代方案,如线性矩阵不等式 (LMI) 工具箱.
主要方法:
- 使用分数计算对FDNN稳定性的理论分析.
- 应用分布式优化 (DOP) 模型来解决代数不等式.
- 为DOP模型开发一种神经动力学解决方法.
- 利用激活函数的几何特性来确保多个APO.
主要成果:
- 建立了FDNN中APO多重米塔格-勒弗勒稳定性的新理论结果.
- 证明具有特定激活功能的FDNN可以拥有多个稳定的APO.
- 展示了DOP方法在解决复杂的稳定性条件和减少计算负载方面的有效性.
- 通过模拟和实验示例验证了理论发现.
结论:
- 拟议的理论框架将稳定性分析扩展到FDNN中的多个APO.
- 分布式优化方法为高维度FDNN提供了一个计算效率高的解决方案.
- 这些发现有助于更深入地了解分数级神经网络的稳定性及其应用,例如关联记忆.
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