Identifiability of dynamical networks with partial node measurements

TL;DR

This paper investigates the conditions under which a dynamical network's topology and transfer functions can be identified from partial node measurements, assuming known topology and external excitations, using graph theory.

Contribution

It provides the first results for network identifiability with partial measurements, relying on graph properties and known topology assumptions.

Findings

Network can often be identified with limited node measurements.

Identifiability depends on the graph paths linking nodes to measured signals.

Results apply when network topology and external excitations are known.

Abstract

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear transfer functions and are excited by known external excitation signals and/or unknown noise signals. A major research question concerns the identifiability of the whole network - topology and all transfer functions - from the measured node signals and external excitation signals. So far all results on this topic have assumed that all node signals are measured. This paper presents the first results for the situation where not all node signals are measurable, under the assumptions that (1) the topology of the network is known, and (2) each node is excited by a known external excitation. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. A practical outcome is that, under those assumptions, a network can often be identified using only a small subset of node measurements.