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 - 2022/2/1
Y1 - 2022/2/1
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
KW - Networked control systems
KW - Graph theory
KW - System identification
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 - 67
SP - 692
EP - 705
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 2
ER -