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

Shengling Shi; Xiaodong Cheng; Paul M.J. Van den Hof

doi:10.1016/j.automatica.2021.110093

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

Shengling Shi
, Xiaodong Cheng
, Paul M.J. Van den Hof (Corresponding author)

Research output: Contribution to journal › Article › Academic › peer-review

13 Citations (Scopus)

122 Downloads (Pure)

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.

Original language	English
Article number	110093
Number of pages	14
Journal	Automatica
Volume	137
DOIs	https://doi.org/10.1016/j.automatica.2021.110093
Publication status	Published - Mar 2022

Bibliographical note

Funding Information:
This project has received funding from the European Research Council (ERC) , Advanced Research Grant SYSDYNET, under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694504 ).

Funding

This project has received funding from the European Research Council (ERC) , Advanced Research Grant SYSDYNET, under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694504 ). The material in this paper was partially presented at the 21st IFAC World Congress (IFAC 2020), July 12–17, 2020, Berlin, Germany. This paper was recommended for publication in revised form by Associate Editor Gianluigi Pillonetto under the direction of Editor Torsten Söderström. This project has received funding from the European Research Council (ERC), Advanced Research Grant SYSDYNET, under the European Union's Horizon 2020 research and innovation programme (grant agreement No 694504). The material in this paper was partially presented at the 21st IFAC World Congress (IFAC 2020), July 12?17, 2020, Berlin, Germany. This paper was recommended for publication in revised form by Associate Editor Gianluigi Pillonetto under the direction of Editor Torsten S?derstr?m.

Funders	Funder number
European Union's Horizon 2020 - Research and Innovation Framework Programme
European Union's Horizon 2020 - Research and Innovation Framework Programme
European Union's Horizon 2020 - Research and Innovation Framework Programme	694504

Keywords

Dynamic networks
Graph theory
Identifiability
System identification

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10.1016/j.automatica.2021.110093

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title = "Generic identifiability of subnetworks in a linear dynamic network: The full measurement case",

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.",

keywords = "Dynamic networks, Graph theory, Identifiability, System identification",

author = "Shengling Shi and Xiaodong Cheng and \{Van den Hof\}, \{Paul M.J.\}",

note = "Funding Information: This project has received funding from the European Research Council (ERC) , Advanced Research Grant SYSDYNET, under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement No 694504 ). ",

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AU - Cheng, Xiaodong

AU - Van den Hof, Paul M.J.

N1 - Funding Information: This project has received funding from the European Research Council (ERC) , Advanced Research Grant SYSDYNET, under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694504 ).

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

KW - Dynamic networks

KW - Graph theory

KW - Identifiability

KW - System identification

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

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