Identifiability of dynamical networks with partial node measurements
For researchers in system identification and network analysis, this work addresses the practical bottleneck of partial measurements, providing first theoretical results and showing that full measurement is often unnecessary.
This paper extends identifiability results for dynamical networks to the case where not all node signals are measurable, showing that under known topology and external excitation, transfer functions can be identified using only a subset of node measurements, with identifiability depending on graph topology.
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.