The collision-avoiding flocking of a Cucker–Smale model with pinning control and external perturbation

Abstract

The Cucker–Smale model is an essential and effective tool for analyzing flocking behavior. A modified Cucker–Smale model with pinning control and external perturbation is proposed in this paper. Primarily, by imposing appropriate restrictions on external perturbation, the system can achieve asymptotic flocking; simultaneously, pinning control improves the speed of flocking. Furthermore, collision-avoiding between any two agents in the flocking process can be derived. The results show that the convergence time depends on control parameters and the convergence speed of the perturbation. Lastly, some numerical simulations are given to illustrate the effectiveness of the theoretical results.