Average State Estimation in Large-Scale Clustered Network Systems

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.