Leader selection for strong structural controllability of single-integrator multi-agent systems

This paper addresses the leader selection problem for strong structural controllability (SSC) of multi-agent systems (MASs). For a path-bud graph, it is proved that only one leader is required to guarantee the SSC of MASs. For a special type of topologies, based on the partition of the topology into disjoint pathes and path-buds, it is proved that the MASs is strongly structurally controllable if the root nodes of the pathes are selected as leaders. For general topologies, an algorithm is provided to determine the agents that can behave as leaders. For some special topologies, the minimum number of leaders guaranteeing the robust strong structural controllability (RSSC) of MASs is also obtained. Two examples are given to verify the effectiveness of the results.