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 G 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 ensures the identifiability of the edge weights of 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 illustrative examples.

Highlights

  • A Global Identifiability Condition for Consensus Networks with Tree GraphsAbstract— 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

  • In order to design and analyze monitoring and control algorithms for a networked dynamic system (NDS) using model based approaches, system identifiability is an important question, i.e., whether the dynamic model of the network can be identified uniquely using available input-output data

  • Relationships between the transfer function of an unweighted graph and its structural properties have been presented in [17]. Another interesting result is presented in [18], where the objective is to detect the loss of an edge in a graph using statistical estimation methods such as maximum a posteriori estimation. In contrast to these results, in this paper we present a sufficient condition on identifiability of weighted graphs from a completely geometric point of view

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Summary

A Global Identifiability Condition for Consensus Networks with Tree Graphs

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 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 G in terms of the associated transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge weights.

INTRODUCTION
PRELIMINARIES
PROBLEM FORMULATION
Main Result
Number of sensors needed
Example
More Information About the Edge-Weights from a Transfer Function
EXAMPLES
Illustrating the one-to-one mapping between weights and the Markov parameters
Sufficiency vs Necessity
A NOTE ON STAR GRAPHS
CONCLUSIONS
Full Text
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