论文标题
通过笛卡尔产品恢复复合网络的结构可观察性
Recovering the Structural Observability of Composite Networks via Cartesian Product
论文作者
论文摘要
可观察性是系统推理和估计中的基本概念。本文重点介绍了笛卡尔产品网络的结构可观察性分析。笛卡尔产品网络在包括并行和分布式系统在内的多种应用中出现。我们提供了一种结构方法，以扩展组成网络（称为因子网络）的结构可观察性到笛卡尔产品网络的结构性可观察性。结构方法基于图理论，是通用的。我们介绍了与网络的结构可观察性密切相关的某些结构，即父母紧密相互联系的组件（母体SCC），父节点和收缩。结果表明，对于特定类型的网络（例如，包含收缩的网络），可以通过笛卡尔产品回收因子网络的结构可观察性。换句话说，如果一个因素网络在结构上是缺陷的，则使用包含跨越周期家族的另一个因子网络，则两个NWTWorks的笛卡尔产物在结构上是完整的。我们为结构可观察性恢复定义了某些网络结构。另一方面，我们根据因素网络中的观察者节点的数量来得出在笛卡尔产品网络中在笛卡尔产品网络中测量其状态的节点的数量。一个示例说明了本文中的图理论分析。
Observability is a fundamental concept in system inference and estimation. This paper is focused on structural observability analysis of Cartesian product networks. Cartesian product networks emerge in variety of applications including in parallel and distributed systems. We provide a structural approach to extend the structural observability of the constituent networks (referred as the factor networks) to that of the Cartesian product network. The structural approach is based on graph theory and is generic. We introduce certain structures which are tightly related to structural observability of networks, namely parent Strongly-Connected-Component (parent SCC), parent node, and contractions. The results show that for particular type of networks (e.g. the networks containing contractions) the structural observability of the factor network can be recovered via Cartesian product. In other words, if one of the factor networks is structurally rank-deficient, using the other factor network containing a spanning cycle family, then the Cartesian product of the two nwtworks is structurally full-rank. We define certain network structures for structural observability recovery. On the other hand, we derive the number of observer nodes--the node whose state is measured by an output-- in the Cartesian product network based on the number of observer nodes in the factor networks. An example illustrates the graph-theoretic analysis in the paper.
