时序超图的能控性与能观性
Controllability and Observability of Temporal Hypergraphs
AI总结：
本文利用张量和非线性系统理论，将能控性与能观性概念推广至时序超图，建立基于张量的秩条件以判定其弱能控性与能观性，并通过合成与真实数据验证了该框架。
摘要：
许多复杂系统，如生态网络、基因组接触网络和社交网络，展现出高阶和时变特性，这些特性可以使用时序超图进行有效建模。然而，由于其固有的时变和非线性特性，分析和控制时序超图提出了重大挑战，而现有的大多数方法主要针对静态超图。在本文中，我们利用张量和非线性系统理论，将能控性和能观性的概念推广到时序超图。具体而言，我们建立了基于张量的秩条件，以确定时序超图的弱能控性和能观性。所提出的框架进一步通过合成和真实世界的例子进行了演示。
英文摘要：
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs. However, analyzing and controlling temporal hypergraphs poses significant challenges due to their inherent time-varying and nonlinear nature, while most existing methods predominantly target static hypergraphs. In this article, we generalize the notions of controllability and observability to temporal hypergraphs by leveraging tensor and nonlinear systems theory. Specifically, we establish tensor-based rank conditions to determine the weak controllability and observability of temporal hypergraphs. The proposed framework is further demonstrated with synthetic and real-world examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
