Reverse Group Consensus of Multi-Agent Systems in the Cooperation-Competition Network

In this paper, a reverse group consensus problem is investigated for the dynamic agents with the inputs in the cooperation-competition network which can be divided into two sub-networks. The weights between the agents in the same sub-network are positive, while the weights between the agents among different sub-networks are negative. Then, the reverse group consensus is firstly studied without the in-degree balance condition. By defining the mirror graph and establishing the solution of the multi-agent system, it is found that the reverse group consensus problem can be achieved if the mirror graph is strongly connected. The explicit expression of the error level is also derived, which would be vanished for multi-agent systems with some special kinds of inputs. Furthermore, as an extension, the decomposing of the cooperation-competition network is discussed, where the concept of the condensation undirected graph and the path balance condition are defined, and several effective sufficient conditions are obtained. Finally, numerical simulation demonstrates the effectiveness of the theoretical analysis.