Bipartite containment tracking in second-order multi-agent systems over switching cooperation-competition networks

The bipartite containment tracking control of second-order multi-agent systems over arbitrarily switching cooperation-competition networks is discussed in this paper. In this case, the followers are divided into two subgroups, which are cooperative within the same subgroup and competitive between the two subgroup. In addition, the leaders have a common sense of cooperation with the followers within one of the subgroups and competition or non-communication with the followers within another subgroup. With the sufficient connectivity condition being given, the fact that the followers who cooperate with the leaders will gradually enter the real convex hull formed by the leaders, and the followers who compete with the leaders will enter a virtual convex hull which is symmetrical with the real convex hull, is proved theoretically. It is also shown that the followers will keep moving in time after entering the convex hulls. Finally, the bipartite containment tracking performances proved by theory are verified by a simulation example.