Consensus tracking for multi-agent systems with directed graph via distributed adaptive protocol

The consensus tracking problem is investigated for multi-agent systems with directed graph. To avoid using any global information, a novel adaptive protocol is proposed based only on the relative state information. A monotonically increasing function for each agent is inserted into the protocol to provide extra freedom for design. By using matrix theory and appropriate Lyapunov techniques, it is shown that the consensus tracking can be achieved in a fully distributed fashion if agents׳ dynamics are stabilizable and the topological graph contains a directed spanning tree with the leader as the root node. A simulation example shows the effectiveness of the design method.