Observer-based tracking problem of leader-follower multi-agent systems

In this paper, we consider the tracking problem for leader-follower multi-agent systems moving in the plane. In our model, the system matrix of the leader can be of any form and the control input of the leader is not known to the followers even if they are connected to the leader. To track such a leader, an observer-based decentralized feedback controller is designed for each follower. We show that if the adjacent graph of the system is connected, with the proposed control law, all the followers can track the leader eventually. At last, we generalize the result to the higher dimension case for some special system matrix of the leader.