Dealing with the flocking problems of Cucker–Smale systems is a challenging issue. In this paper, the finite-time and fixed-time flocking problems of the Cucker–Smale system are investigated. By designing new continuous non-Lipschitz pinning controllers and using the theory of differential equations, sufficient conditions for the flocking of Cucker–Smale systems are obtained. Besides, sufficient conditions are given to ensure that there is no collision during the process of flocking. The effect of control parameters on the convergence speed is also investigated. The results show that the convergence time is related to control parameters and the density of pinned nodes. Finally, some numerical simulations are used to verify the theoretical results.

处理 Cucker-Smale 系统的集群问题是一个具有挑战性的问题。本文研究了 Cucker-Smale 系统的有限时间和固定时间植绒问题。通过设计新的连续非Lipschitz pinning控制器并利用微分方程理论，获得了Cucker-Smale系统植绒的充分条件。此外，还提供了充分的条件来保证植绒过程中不发生碰撞。还研究了控制参数对收敛速度的影响。结果表明，收敛时间与控制参数和固定节点的密度有关。最后，通过一些数值模拟来验证理论结果。