Generic identifiability of subnetworks in a linear dynamic network: the full measurement case

TL;DR

This paper establishes conditions under which subnetworks in linear dynamic networks can be generically identified from measured signals, even with partial measurements and known fixed modules, enabling efficient network identification.

Contribution

It develops new path-based conditions for generic identifiability of subnetworks with full measurements, including fixed modules, and proposes synthesis methods for excitation signal allocation.

Findings

Path-based conditions for generic identifiability are derived.

Synthesis results for excitation signal placement are provided.

A generalized indirect identification algorithm is proposed.

Abstract

Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions for generic identifiability of multiple modules, i.e. a subnetwork, are developed for the situation that all node signals are measured and excitation of the network is provided by both measured excitation signals and unmeasured disturbance inputs. Additionally, the network model set is allowed to contain non-parametrized modules that are fixed, and e.g. reflect modules of which the dynamics are known to the user. The conditions take the form of path-based conditions on the graph of the network model set. Based on these conditions, synthesis results are formulated for allocating external excitation signals to achieve generic identifiability of particular subnetworks. If there are a sufficient number of measured external excitation signals, the formulated results give rise to a generalized indirect type of identification algorithm that requires only the measurement of a subset of the node signals in the network.