Distributed Prescribed-Time Formation Tracking for General Linear Multiagent Systems

This paper studies prescribed-time formation tracking problems for general linear multiagent systems with a leader of unknown input. First, by introducing a time-varying parametric Lyapunov equation, a distributed prescribed-time formation tracking protocol is proposed for each follower to accomplish an expected formation within a prescribed time, and simultaneously follow the leader's state trajectory. Then, adaptive gains are developed to achieve formation tracking in a fully distributed manner and to compensate for the leader's unknown input. Furthermore, the prescribed-time convergence of the formation tracking error is analyzed using Lyapunov theories. Finally, the effectiveness of theoretical results is validated through a simulation example.