Abstract: Due to the impact of the environment and the fact that it can merely influence other agents at a limited speed, the impact of the multi-agent does not work immediately. Therefore, for the most part, there is a certain time delay. Consequently this paper concludes that when the other system parameters are constant, the smaller the coupling coefficient is, the greater communication delay the system can tolerate. This further proves the correctness of the theory. Based on Cucker-Smale model, this paper studies the communication system with time delay, mainly by employing the quadratic function theory to prove that through meeting certain conditions, the communication delay between agents can do the cluster motion. At the end of this paper, the numerical simulation results of Cucker-Smale model with communication delay are also elaborately listed.

Key words: flocking, multi-agent, communication delay

摘要： 由于环境的影响以及自身只能以有限的速度影响其他智能体，使得多智能体之间的影响不能立即作用，因此通常都有一定的时间延迟。在Cucker-Smale模型的基础之上研究了带有通信时滞的系统，主要利用二次函数理论证明了当智能体间的通信时滞在满足一定的条件下，依然可以达到群集运动。最后也给出了通信时滞下的Cucker-Smale模型的数值仿真结果，发现当其他系统参数不变时，耦合系数越小，系统能容忍的通信时滞越大。这也进一步证明了该理论的正确性。

关键词: 群集运动, 多智能体系统, 通信时滞