Gramian-informed框架用于对抗节点攻击的边流网络分析
Gramian-Informed Framework for Edge Flow Network Analysis Against Nodal Attacks
- Indraprastha Institute of Information Technology（印度信息技术学院）
- National Laboratory of the Rockies（落基山国家实验室）
- University of California, San Diego（加州大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于Gramian的框架，通过脆弱性矩阵分析节点输入对边流的一阶影响，并在有向线网络和随机网络上验证了其与传统性能指标的一致性。
AI中文摘要：
我们通过可控性Gramian研究节点输入对网络系统边流的一阶效应。我们考虑离散时间和连续时间动力学，并受脉冲和阶跃输入扰动的影响。为了表征它们对网络行为的影响，我们引入了脆弱性矩阵（VM）的概念，并提供了基于Gramian的显式表达式，揭示了网络拓扑与动力学之间相互作用所起的关键作用。对于有向线网络类，我们根据边权重、输入持续时间和到节点输入的图距离，具体化了这些闭式表达式。在有向线和随机Erdős-Rényi网络上的数值模拟表明，通过VM识别的影响节点与传统时域性能指标（如$\mathscr{H}_2$和$\mathscr{H}_{\infty}$）之间存在紧密对应关系。
英文摘要：
We study the first-order effects of nodal inputs on edge flows of network systems through controllability Gramians. We consider both discrete- and continuous-time dynamics subject to impulse and step input disturbances. To characterize their impact on network behavior, we introduce the notion of a vulnerability matrix (VM) and provide explicit Gramian-based expressions that reveal the critical role played by the interplay between network topology and dynamics. For the class of directed line networks, we particularize these closed-form expressions in terms of edge weights, input duration, and graph distance to the nodal input. Numerical simulations on directed line and random Erdős-Rényi networks show a tight correspondence between influential nodes identified with the VM and conventional time-domain performance metrics, such as $\mathscr{H}_2$ and $\mathscr{H}_{\infty}$.
