In this paper, we address the fixed-time consensus tracking problem of second-order leader-follower multi-agent systems with nonlinear dynamics under directed topology. The consensus tracking algorithm consists of distributed observer and observer-based decentralized controller. The fixed-time distributed observer guarantees that each follower estimates the leader’s state under directed topology within a fixed time, where the upper bound of convergence time is independent on the initial conditions. The fixed-time decentralized controller makes each follower converge to the leader’s state in fixed time via tracking the distributed observer’s state and overcome the nonlinear dynamics without adding linear control terms. Finally, the numerical example is provided to illustrate the effectiveness of the results.

在本文中，我们解决了在有向拓扑下具有非线性动力学的二阶领导者-跟随者多智能体系统的固定时间一致性跟踪问题。共识跟踪算法由分布式观察者和基于观察者的分散控制器组成。固定时间分布式观察器保证每个跟随者在固定时间内估计有向拓扑下领导者的状态，其中收敛时间的上限与初始条件无关。固定时间分散控制器通过跟踪分布式观察者的状态，在不增加线性控制项的情况下，使每个跟随者在固定时间内收敛到领导者的状态，克服非线性动力学。最后，给出数值例子来说明结果的有效性。