Finite-time consensus tracking for multi-agent systems with settling time estimation

This paper investigates the distributed finite-time consensus tracking problem for a group of autonomous agents modeled by double-integrator dynamics under a leader with non-zero acceleration. First of all, a distributed finite-time consensus tracking protocol is proposed based on the relative position and relative velocity measurements. By using a Lyapunov function, it is shown that distributed consensus tracking can be achieved in finite time under the condition that the acceleration of the leader is bounded but not available to followers. In particular, the settling time can be estimated efficiently by computing the value of the Lyapunov function at the initial point. Then, a new observer-based algorithm is designed to solve the finite-time consensus tracking problem when the relative velocity measurements are not available to the agents. It is proved that the states of the followers can move to that of 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. Finally, the effectiveness of the algorithms is illustrated by numerical simulations.