The role of arc rotation on improving consensus convergence rate for a leader-follower multi-agent system

The problem of arc rotation operations to improve the consensus convergence rate of multi-agent systems with strongly connected directed graphs as follower interaction topologies is considered in this paper. For fixing the head of a fixed arc and rotating the arc, some necessary and sufficient conditions are provided for effective arc rotation. In the case of arc rotation where the tail of the arc is fixed, some necessary conditions for effective arc rotation have been presented. In the case where the interaction topology of a multi-agent system can be divided into blocks with equal row sums through a layer-by-layer partitioning approach, if the head of the rotating arc is fixed, then the effective arc rotation operation can be determined by the tail layers of the arc. If the tail of the arc is fixed, the effective arc rotation operation can be determined by the head and tail layers of the arc. Ultimately, several numerical experiments are carried out to confirm the validity of the theoretical results.