For the monitoring of large-scale clustered network systems (CNS), it suffices in many applications to know the aggregated states of given clusters of nodes. This article provides necessary and sufficient conditions such that the average states of the prespecified clusters can be reconstructed and/or asymptotically estimated. To achieve computational tractability, the notions of average observability and average detectability of the CNS are defined via the projected network system, which is of tractable dimension and is obtained by aggregating the clusters. The corresponding necessary and sufficient conditions of average observability and average detectability are provided and interpreted through the underlying structure of the induced subgraphs and the induced bipartite subgraphs, which capture the intracluster and intercluster topologies of the CNS, respectively. Moreover, the design of an average state observer, whose dimension is minimum and equals the number of clusters in the CNS, is presented.

中文翻译：

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大规模集群网络系统中的平均状态估计

对于大型群集网络系统（CNS）的监视，在许多应用程序中只要知道节点给定群集的聚集状态就足够了。本文提供了必要和充分的条件，以便可以重新构造和/或渐近估计预定簇的平均状态。为了实现计算可处理性，CNS的平均可观察性和平均可检测性的概念是通过投影网络系统定义的，该网络具有可处理的维度，并且是通过聚集群集而获得的。通过诱导子图和诱导二分图的基本结构，提供并解释了平均可观察性和平均可检测性的相应必要条件和充分条件，它们分别捕获了CNS的集群内和集群间拓扑。此外，提出了一个平均状态观测器的设计，该观测器的尺寸最小并且等于CNS中的簇数。