A Global Identifiability Condition for Consensus Networks with Tree Graphs

TL;DR

This paper establishes a sufficient condition for the identifiability of edge weights in linear consensus networks with tree structures, enabling effective sensor placement for parameter estimation.

Contribution

It introduces a new identifiability condition for acyclic network graphs and proposes a sensor placement algorithm to ensure edge weight identifiability.

Findings

Derived a condition linking transfer functions to edge weight identifiability.

Proposed a sensor placement algorithm guaranteeing identifiability.

Validated results with illustrative examples.

Abstract

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