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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.

Collision avoiding finite-time and fixed-time flocking of Cucker–Smale systems with pinning control