Prescribed-Time Time-Varying Formation Tracking of Linear Multiagent Systems With Multiple Leaders on Directed Graphs: A Fully Distributed Technique
研究了有向交互下一般线性系统的时变编队跟踪问题，提出一种全分布式预设时间控制协议，无需全局拓扑信息和领导者输入上界，适用于多领导者场景。
In this article, fully distributed prescribed-time control methods for time-varying formation tracking problems of general linear systems with directed interactions are investigated. The considered leaders have nonzero control inputs, whose upper bounds are initially unknown to the followers. For the given multiple-leader scenario, a formation tracking protocol is designed, which incorporates three components: a distributed controller, an adaptive law, and a distributed estimator. Specifically, based on the adaptive technique, the controller can be implemented without requiring global topology knowledge and the leaders’ input bounds. The estimator can also be executed in a distributed fashion, and algebraic loop phenomena are avoided herein. To guarantee prescribed-time convergence of the controller and estimator, two time-varying parameters are designed. Rigorous convergence analyses are conducted using Lyapunov functions and parametric Lyapunov equations. Furthermore, to tackle typical numerical implementation issues associated with prescribed-time control methods, a modified version of the protocol is presented. Finally, simulation examples are provided to verify the proposed theoretical results.