Structural Controllability of Symmetric Networks

The theory of structural controllability allows us to assess controllability of a network as a function of its interconnection graph and independently of the edge weights. Yet, existing structural controllability results require the weights to be selected arbitrarily and independently from one anoth...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 64; no. 9; pp. 3740 - 3747
Main Authors Menara, Tommaso, Bassett, Danielle S., Pasqualetti, Fabio
Format Journal Article
LanguageEnglish
Published New York IEEE 01.09.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Biology
Constraints
Controllability
Graph theory
Indexes
interconnected systems
Matrices
network controllability
Networks
Observability
structural controllability
Symmetric matrices
symmetric networks
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Summary:The theory of structural controllability allows us to assess controllability of a network as a function of its interconnection graph and independently of the edge weights. Yet, existing structural controllability results require the weights to be selected arbitrarily and independently from one another and provide no guarantees when these conditions are not satisfied. In this note, we develop a new theory for structural controllability of networks with symmetric, thus constrained, weights. First, we show that network controllability remains a generic property even when the weights are symmetric. Then, we characterize necessary and sufficient graph-theoretic conditions for structural controllability of networks with symmetric weights: a symmetric network is structurally controllable if and only if it is structurally controllable without weight constraints. Finally, we use our results to assess structural controllability from one region of a class of empirically-reconstructed brain networks.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2881112