Consistency Of Two Kinds Of Multi - Agent Systems In Graphs

As we all known, the consensus problem of multi-agent systems has become more and more popular for its potential applications in broad areas in the last decade. We can divide existing consensus problem into two classes. namely, consensus with a leader(it is both named leader-follower consensus and distributed tracking), or consensus without a leader(i.e.leaderless consensus). Previous works alone this line are mainly for some specific systems, whose communication topology graphs are undirected, or the leader-follower system whose subgraphs among its followers are undirected. However, the Laplacian matrix of directed graph is usually asymmetric, which makes it far more difficult to construct right consensus protocol and select suitable Lyapunov function candidate. To overcome the limitation, we introduce a monotonically increasing function inspired by [1], [2]and develop a new Lyapunov function to achieve the consensus of two kinds of multi-agent systems with directed graphs. The main results are as follows:1) Distributed adaptive tracking consensus of multi-agent systems with directed graphs in the presence of a leader with unknown bounded input.If the communication topology graphs among the N?1agents are directed, and the graphs include a directed spanning tree with the leader, whose input probably be nonzero and unavailable to any follower. First, by considering the case of leaderless to formulate the problem of leader-follower consensus. Then, by using the ? modification to design a novel adaptive distributed consensus protocol, so that the tracking error is ultimately uniformly bounded, and the coupling gains is as well. As an extension, we consider the containment control problem with multiple leaders. Now, let we suppose that for each follower, there is at least one leader which has a path to that follower. At last, we presented a simulation example to illustrate.2) Distributed adaptive consensus of linear multi-agent systems with directed graphs in the presence of certain external disturbances.If the communication topology graphs among the N agents are directed and strongly connected. In addition, some certain external disturbances exist. First, by considering the case without external disturbance to formulate the problem with external disturbance. Then, by using the ? modification we designed a novel adaptive distributed consensus protocol, so that the adaptive consensus error is ultimately uniformly bounded, and the coupling gains is as well. As an extension, we consider the common multi-agent systems, who is not only with some certain external disturbances but also with a leader whose control input is not zero and unavailable toany follower. Now, suppose that, the communication topology graph includes a directed spanning tree with the leader as its root node, and the communication topology graph among followers is both strongly connected and directed. At last, we presented a simulation example to illustrate.