Leader localization in multi-agent systems subject to failure: A graph-theoretic approach

In this paper, structural controllability of a leader–follower multi-agent system with multiple leaders is studied. A graphical condition for structural controllability based on the information flow graph of the system is provided. The notions of pp-link and qq-agent controllability in a multi-leader setting are then introduced, which provide quantitative measures for the controllability of a system subject to failure in the agents and communication links. The problem of leader localization is introduced, which is concerned with finding the minimum number of agents whose selection as leaders results in a pp-link or qq-agent controllable network. Polynomial-time algorithms are subsequently presented to solve the problem for both cases of undirected and directed information flow graphs.