Allocation of Excitation Signals for Generic Identifiability of Linear Dynamic Networks

TL;DR

This paper introduces a graph-based method for optimally placing excitation signals in linear dynamic networks to ensure their generic identifiability, using novel pseudotree structures and an algorithmic decomposition approach.

Contribution

It proposes a new graph structure called directed pseudotree and an algorithm to decompose extended graphs for optimal excitation signal placement in network identification.

Findings

The method guarantees generic identifiability with minimal excitation signals.

The approach can be adapted for measurement signal placement using anti-pseudotrees.

Algorithmic decomposition efficiently identifies optimal excitation locations.

Abstract

A recent research direction in data-driven modeling is the identification of dynamic networks, in which measured vertex signals are interconnected by dynamic edges represented by causal linear transfer functions. The major question addressed in this paper is where to allocate external excitation signals such that a network model set becomes generically identifiable when measuring all vertex signals. To tackle this synthesis problem, a novel graph structure, referred to as \textit{directed pseudotree}, is introduced, and the generic identifiability of a network model set can be featured by a set of disjoint directed pseudotrees that cover all the parameterized edges of an \textit{extended graph}, which includes the correlation structure of the process noises. Thereby, an algorithmic procedure is devised, aiming to decompose the extended graph into a minimal number of disjoint pseudotrees, whose roots then provide the appropriate locations for excitation signals. Furthermore, the proposed approach can be adapted using the notion of \textit{anti-pseudotrees} to solve a dual problem, that is to select a minimal number of measurement signals for generic identifiability of the overall network, under the assumption that all the vertices are excited.