Identifiability of dynamic networks: the essential r\^ole of dources and dinks

TL;DR

This paper extends the understanding of dynamic network identifiability by introducing the concepts of dources and dinks, showing their critical roles in excitation and measurement patterns necessary for guaranteeing generic identifiability.

Contribution

It identifies the roles of dources and dinks in dynamic networks and establishes new necessary conditions for generic identifiability beyond previous criteria.

Findings

Dources must be excited for identifiability.

Dinks must be measured for identifiability.

Sources and sinks have specific excitation and measurement requirements.

Abstract

The paper [1] presented the first results on generic identifiability of dynamic networks with partial excitation and partial measurements, i.e. networks where not all nodes are excited or not all nodes are measured. One key contribution of that paper was to establish a set of necessary conditions on the excitation and measurement pattern (EMP) that guarantee generic identifiability. In a nutshell, these conditions established that all sources must be excited and all sinks measured, and that all other nodes must be either excited or measured. In the present paper, we show that two other types of nodes, which are defined by the local topology of the network, play an essential r\^ole in the search for a valid EMP, i.e. one that guarantees generic identifiability. We have called these nodes dources and dinks. We show that a network is generically identifiable only if, in addition to the above mentioned conditions, all dources are excited and all dinks are measured. We also show that sources and dources are the only nodes in a network that always need to be excited, and that sinks and dinks are the only nodes that need to be measured for an EMP to be valid.