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Recovering the Structural Observability of Composite Networks via Cartesian Product
IEEE Transactions on Signal and Information Processing over Networks ( IF 3.0 ) Pub Date : 2020-01-16 , DOI: 10.1109/tsipn.2020.2967145
Mohammadreza Doostmohammadian

Observability is a fundamental concept in system inference and estimation. This article 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 networks 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 article.

中文翻译:

通过笛卡尔积恢复复合网络的结构可观性

可观察性是系统推断和估计的基本概念。本文着重于笛卡尔乘积网络的结构可观察性分析。笛卡尔积网络出现在包括并行和分布式系统在内的各种应用中。我们提供了一种结构方法,将组成网络(称为因子网络)的结构可观察性扩展到笛卡尔乘积网络的结构可观察性。结构化方法基于图论并且是通用的。我们介绍与网络的结构可观察性紧密相关的某些结构,即父级强连接组件(父级SCC),父级节点和收缩。结果表明,对于特定类型的网络(例如 包含收缩的网络)可以通过笛卡尔积恢复因子网络的结构可观察性。换句话说,如果其中一个因子网络在结构上排名不足,则使用包含跨度周期族的另一个因子网络,则两个网络的笛卡尔积在结构上是完全排名。我们定义某些网络结构以进行结构可观察性恢复。另一方面,我们基于因子网络中观察者节点的数量,得出笛卡尔积网络中观察者节点的数量(该节点的状态通过输出进行测量)。一个示例说明了本文中的图论分析。如果使用包含跨度周期族的另一个因子网络,则两个网络的笛卡尔积在结构上是满秩的。我们定义某些网络结构以进行结构可观察性恢复。另一方面,我们基于因子网络中观察者节点的数量,得出笛卡尔积网络中观察者节点的数量(该节点的状态通过输出进行测量)。一个示例说明了本文中的图论分析。如果使用包含跨度周期族的另一个因子网络,则两个网络的笛卡尔积在结构上是满秩的。我们定义某些网络结构以进行结构可观察性恢复。另一方面,我们基于因子网络中观察者节点的数量,得出笛卡尔积网络中观察者节点的数量(该节点的状态通过输出进行测量)。一个示例说明了本文中的图论分析。
更新日期:2020-04-22
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