TY - JOUR

T1 - Allocation of Excitation Signals for Generic Identifiability of Linear Dynamic Networks

AU - Cheng, Xiaodong

AU - Shi, Shengling

AU - Van den Hof, Paul M.J.

PY - 2021

Y1 - 2021

N2 - 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 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 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 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.

AB - 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 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 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 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.

KW - Analytical models

KW - Correlation

KW - Covariance matrices

KW - Network topology

KW - Noise measurement

KW - Power system dynamics

KW - Topology

UR - http://www.scopus.com/inward/record.url?scp=85100486022&partnerID=8YFLogxK

U2 - 10.1109/TAC.2021.3053540

DO - 10.1109/TAC.2021.3053540

M3 - Article

AN - SCOPUS:85100486022

VL - XX

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - XX

ER -