The fixed-time flocking of multi-agent systems with a virtual leader is investigated in this paper. The motion dynamics of the agents are assumed to be unknown and only satisfy the boundedness, which does not need to be modelled by the Lipschitz condition. To achieve the flocking and collision avoidance for all agents in the fixed time, a control protocol in the high-dimensional space is developed by using the graph theory and the theoretical properties of differential equations. Moreover, the upper bound of the settling time only depending on the control protocol and the topology of network is estimated. Numerical examples are used to verify the theoretical results, and show that the proposed method provides an applicable method for the control of the nonlinear dynamic systems.

本文研究了具有虚拟领导者的多主体系统的定时植绒。假定代理的运动动力学是未知的，并且仅满足有界度，这不需要通过Lipschitz条件进行建模。为了在固定时间内实现所有智能体的植绒和避免碰撞，利用图论和微分方程的理论性质，开发了高维空间中的控制协议。而且，仅根据控制协议和网络拓扑来估计建立时间的上限。数值算例验证了理论结果，表明所提出的方法为非线性动力学系统的控制提供了一种适用的方法。