Structural controllability of multi-agent networks: Importance of individual links

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied from a graph-theoretic point of view. The effects of the loss of agents and communication links on the controllability of an information flow graph are previously studied. In this work, the corresponding results are exploited to introduce some useful indices and importance measures that help characterize and quantify the role of individual links in the controllability of the overall network. To this end, the problem of preservation of structural controllability under link failures is considered as a gateway for evaluation and comparison of the contributions made by various links in the network. A number of examples are exploited throughout the paper to elaborate on the analytical findings and demonstrate the applicability of the proposed measures.