Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration

This paper addresses the distributed finite-time tracking problem for a group of mobile agents modeled by double-integrator dynamics under a leader with bounded unknown acceleration. First, a distributed finite-time tracking protocol is designed based on both the relative position and the relative velocity measurements. This protocol can drive the states of the followers to track the leader in finite time under the constraint that the leader's acceleration is bounded but unknown to the followers. Then, a novel position-based tracking protocol is designed and analyzed for solving the distributed finite-time tracking problem when both velocity and acceleration measurements are not available for the followers. It is theoretically proved that the followers can move to be with the leader in finite time if the network topology is undirected among the followers but has a directed path from the leader to each follower. In particular, the position-based protocol does not require the relative input information between the agents. Finally, the effectiveness of the algorithms is illustrated by numerical simulations.