On leaderless and leader-following consensus for interacting clusters of second-order multi-agent systems

This paper investigates the group consensus phenomenon for multiple interacting clusters of double-integrator agents in the presence of both cooperative and competitive inter-cluster couplings under two different frameworks, viz., the framework that all agents share the same position and velocity interaction topology and the framework that the position and velocity topologies are modeled by totally independent graphs. Both the case without leaders and the leader-following (meaning there is a single leader for each cluster of agents) case are systematically investigated. Different systems models are systematically analyzed accordingly using various different techniques. Theoretical analysis shows that for most cases, there holds a consistent structural result that group consensus can be achieved if the underlying topology for each cluster of agents satisfies certain connectivity assumptions and further, the intra-cluster couplings are sufficiently strong. Some lower bounds for such strengths are explicitly specified as well.