This paper addresses the problem of consensus tracking with fixed-time convergence, for leader–follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.

本文针对具有双重集成者动态的领导者跟随者多主体系统，解决了具有固定时间收敛性的共识跟踪问题，在该系统中，只有一部分关注者可以访问领导者的状态。控制方案分为两个步骤。第一个专用于每个跟随者以分布式方式和固定时间估算领导者状态。然后，基于对领导者状态的估计，每个跟随者都会计算其控制律以在固定时间内跟踪领导者。本文研究并比较了两种控制策略，以解决上述两个步骤。第一个是自主协议，可确保观察者和控制器部件的固定时间收敛，在该时间，用户可以优先设置建立时间的上限（UBST）。然后，以前的策略是使用时变增益重新设计的，以获得非自治协议。这使得可以获得对UBST的保守估计较少，同时保证时变收益仍然有限。一些数值示例表明了所提出共识协议的有效性。