利用笛卡尔积恢复复合网络的结构可观性
Recovering the Structural Observability of Composite Networks via Cartesian Product
摘要：
可观测性是系统推理和估计中的一个基本概念。本文主要研究笛卡尔积网络的结构可观性分析。笛卡尔积网络出现在各种应用中，包括并行和分布式系统。我们提供了一个结构的方法来扩展的组成网络（称为因子网络）的笛卡尔积网络的结构可观性。结构化的方法是基于图论和通用。我们引入了一些与网络的结构可观性密切相关的结构，即父强连通分量（父SCC），父节点和收缩。结果表明，对于特定类型的网络（如包含收缩的网络），因子网络的结构可观性可以通过笛卡尔积来恢复。换句话说，如果其中一个因子网络在结构上是秩亏的，使用另一个包含生成循环族的因子网络，则两个nwwork的笛卡尔积在结构上是满秩的。我们定义了一定的网络结构的结构可观性恢复。另一方面，我们根据因子网络中的观测器节点的数量，推导出笛卡尔乘积网络中的观测器节点的数量--其状态由输出测量的节点。文中以一个实例说明了图论分析方法。
英文摘要：
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.
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