Ordered-Bipartite Consensus of Multi-Agent Systems under Finite Time Control

Since group consensus (GC) control accounts for one-half of the multi-robot coordination domain, as does complete consensus control, this paper will formulate a certain kind of GC and group bipartite consensus (GBC) in finite time for multi-agent systems (MAS). It should be noted that the key to this work is that information transfer under acyclic partition networks is zero-sum between groups and the cooperative–competitive interaction. The general GC will firstly be achieved under acyclic partition, which reflects the fact that such topology allows the MAS to reach agreement in an ordered and hierarchical process. Further, the information communication is zero-sum within each group under the acyclic partition signed digraph. Thus, the group–bipartite agreement for MAS is given under acyclic bipartite topology. These results display not only an ordered, hierarchical state, but also an intra-group symmetric state. In addition, simulation examples are presented in parallel with the theoretical results.