对于两种类型的时间变化延迟的等级稳定性条件 一般化神经网络
IEEE transactions on cybernetics
|July 18, 2024
概括
这项研究为具有时间变化的延迟的通用神经网络 (GNN) 提出了新的层次稳定性标准. 新方法通过使用高阶积分不等式和先进的矩阵技术来改进稳定性分析.
科学领域:
- 控制系统工程 控制系统工程
- 计算神经科学是一种神经科学.
- 应用数学 应用数学 应用数学
背景情况:
- 具有不同时间延迟的通用神经网络 (GNN) 存在稳定性分析挑战.
- 现有的方法通常依赖于低阶积分不等式,这限制了它们的适用性.
- 在实际的 GNN 应用中,获得精确的延迟限制可能很困难.
研究的目的:
- 开发GNN的高级稳定性标准,其延迟时间可变,即使延迟极限是未知的或仅限于上限.
- 克服现有的二阶积分不平等方法的局限性.
- 引入一种用于构建利亚普诺夫-克拉索夫斯基函数 (LKF) 和解决高度多项式负条件 (NC) 的新方法.
主要方法:
- 使用从N级概括的基于自由矩阵的积分不等式 (GFII) 衍生的多个积分来构建层次的利亚普诺夫-克拉索夫斯基函数 (LKF).
- 为2N-1度延迟多项式开发新的修改矩阵多项式负条件 (NCs).
- 制定等级线性矩阵不等式 (LMI) 来解决GFII固有的非线性问题.
主要成果:
- 成功建立了延迟GNN的新型层次稳定性标准.
- 证明了拟议方法在克服与LKF配方和高度多项式NCs相关的挑战方面的有效性.
- 开发的等级LMI有效地解决了GFIIs产生的非线性问题.
结论:
- 与现有方法相比,拟议的等级稳定性标准提供了一种优越的方法来分析GNN的稳定性,其延迟时间可变.
- 该方法为稳定性分析提供了更强大的框架,特别是在延迟信息有限的情况下.
- 数字示例证实了开发的等级稳定性标准的优越性和有效性.
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