Second Order Group Consensus For Multi-agent System

In the past decade, the cooperative control of multi-agent systems(MASs)has drawn much researchers' attention due to its wide applications in cooperative control of unmanned air vehicles, flocking of multiple vehicles, formation control scheduling of automated highway systems and other fields. As the basic problem of MASs, consensus problem aims to guarantee that all the agents reach the same state by using the limited information exchange between individuals to design algorithms. Recently, group/cluster consensus has been pointed out as an im-portant elaboration of the classical consensus problem and attracted a great deal of attention within the control community. Group consensus means that all the agents in MASs are divided into multiple subgroups because of the differences in physical characteristics or task assignments. Moreover, each group asymptotically reaches a consistent state while no consensus appears among different group. In this paper, second-order group consensus are studied under under fixed topolo-gy and switching topology, respectively. Our main results and contributions are summarized as follows:1. The group consensus problem of second-order multi-agent systems under fixed topology with time delays is studied. By Lyapunov first method and Hopf bifurcation theory, respectively, we find the corresponding upper bound of time delay to guarantee the group consensus of MASs. Finally, simulation examples are given to show the effectiveness of the theoretical analysis.2. The group consensus problem of second-order switching linear system-s with average dwell time switching is studied. First, by state transformation method, the group consensus problem of multi-agent systems can be equivalently transformed into the asymptotical stability of a new system. Then, two sufficient criteria are obtained by Lyapunov function method for the underlying systems in both continuous-time and discrete-time contexts. Finally, simulation examples are given to show the effectiveness of the theoretical analysis.