Strong Structural Controllability of Networks under Time-Invariant and Time-Varying Topological Perturbations

This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this direction, we introduce a new construct referred to as a perfect g...

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Bibliographic Details
Published in:arXiv.org 2020-05
Main Authors: Shima Sadat Mousavi, Haeri, Mohammad, Mesbahi, Mehran
Format: Article
Language:English
Subjects:
Controllability
Networks
Robust control
Stability
Upper bounds
Online Access:Get full text
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Summary:This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this direction, we introduce a new construct referred to as a perfect graph associated with a network with a given set of control nodes. The tight upper bounds on the number of edges that can be added to, or removed from a network, while ensuring strong structural controllability, are then derived. Moreover, we obtain a characterization of critical edge-sets, the maximal sets of edges whose any subset can be respectively added to, or removed from a network, while preserving strong structural controllability. In addition, procedures for combining networks to obtain strongly structurally controllable network-of-networks are proposed. Finally, controllability conditions are proposed for networks whose edge weights, as well as their structures, can vary over time.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.09960