Asynchronous bipartite containment control of second-order multi-agent systems under switching topologies

This paper investigates the bipartite containment control problem for second-order multi-agent systems (MASs) via asynchronous sampling under switching topologies, where the relationships of both competition and cooperation exist among agents. Under asynchronous setting, each agent only receives its neighbors' information at its own clock which is independent of the others'. The objective of bipartite containment control is to make the followers converge to a convex hull containing each leader's trajectory as well as its opposite trajectory, which is the same as it in modulus but different in sign. First, the bipartite control problem is transformed into the converge problem of the product of infinite time-varying row stochastic matrices. Then, based on the theoretical tools including graph theory, nonnegative matrix theorem, and composition of binary relation, a sufficient condition is obtained for the bipartite containment control problem. It is shown that with proper parameters, the bipartite containment control can be achieved if the union of topology graphs related to any time intervals with given length has a directed spanning forest. Finally, the validity of the theoretical result under asynchronous sampling is demonstrated by a numerical simulation.