This paper considers the fixed-time control problem of a multi-agent system composed of a class of Euler–Lagrange dynamics with parametric uncertainty and a dynamic leader under a directed communication network. A distributed fixed-time observer is first proposed to estimate the desired trajectory and then a fixed-time robust controller is constructed by transforming uncertain Euler–Lagrange systems into second-order systems and utilizing the backstepping design procedure. The overall design guarantees that the synchronization errors converge to zero in a fixed time independent of initial conditions. The control design conditions can also be relaxed for a weaker finite-time control requirement.

本文考虑了在有向通信网络下由一类具有参数不确定性的欧拉-拉格朗日动力学和动态领导者组成的多智能体系统的固定时间控制问题。首先提出了一个分布式固定时间观测器来估计期望的轨迹，然后通过将不确定的欧拉-拉格朗日系统转换为二阶系统并利用反步设计程序构建一个固定时间鲁棒控制器。整体设计保证同步误差在固定时间内收敛到零，与初始条件无关。对于较弱的有限时间控制要求，也可以放宽控制设计条件。