Recovering Structural Controllability on Erdős-Rényi Graphs via Partial Control Structure Re-Use
Large-scale distributed control systems such as those encountered in electric power networks or industrial control systems must be assumed to be vulnerable to attacks in which adversaries can take over control over at least part of the control network by compromising a subset of nodes. In this paper we study structural controllability properties of the control graph in LTI systems, addressing the question of how to efficiently re-construct a control graph as far as possible in the presence of such compromised nodes.
We study the case of sparse Erdős-Rényi Graphs with directed control edges and seek to provide an approximation of an efficient reconstructed control graph by minimising control graph diameter. As the underlying Power Dominating Set problem does not permit efficient re-computation, we propose to reduce the average-case complexity of the recovery algorithm by re-using remaining fragments of the original, efficient control graph where possible and identifying previously un-used edges to re-join these fragments to a complete control graph, validating that all constraints are satisfied in the process. Whilst the worst-case complexity is not improved, we obtain an enhanced average-case complexity that offers a substantial improvement where sufficiently many fragments of the original control graph remain, as would be the case where an adversary can only take over regions of the network and thereby control graph.
KeywordsStructural controllability Control systems resilience Power Dominating Set
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