A Global Identifiability Condition for Consensus Networks with Tree Graphs

摘要

In this paper we present a sufficient condition that guaranteesidentifiability of linear network dynamic systems exhibiting continuous-timeweighted consensus protocols with acyclic structure. Each edge of theunderlying network graph $\mathcal G$ of the system is defined by a constantparameter, referred to as the weight of the edge, while each node is defined bya scalar state whose dynamics evolve as the weighted linear combination of itsdifference with the states of its neighboring nodes. Following the classicaldefinitions of identifiability and indistinguishability, we first derive acondition that ensure the identifiability of the edge weights of $\mathcal G$in terms of the associated transfer function. Using this characterization, wepropose a sensor placement algorithm that guarantees identifiability of theedge weights. We describe our results using several illustrative examples.