随机交互下Cucker-Smale群体行为模型

群体行为描述了多智能体群仅使用局部信息和简单的作用规则，组织成有序运动的现象。Cucker-Smale(C-S)模型是近年来比较热门的群体行为模型，该模型在生物、物理、控制、计算机科学等领域有着广泛的应用前景。本项目研究随机交互下C-S群体行为模型的相关问题。首先研究一般有向图上具有随机通信范围的C-S模型，在每个时间点智能体与它的邻居通信仅当它们之间的距离不超过它们之间的随机通信范围。其次研究交替根领导下服从随机失败的防碰撞C-S模型，群体的根领导在智能体间时不时地进行切换，并且在任意时刻智能体间都存在最小正距离。最后研究随机交互下具有奇异权函数的C-S模型，每个智能体在每个时间点都有可能接收不到它邻居集中智能体的信息，并且智能体间是防碰撞的，否则权函数的值将趋于无穷。本课题旨在通过对上述问题的研究，建立只依赖于初始状态和系统参数的收敛结果，使C-S模型具有更强的应用性。

Flocking represents the phenomena that agents, using only limited information and simple rules, organize into an ordered motion. The C-S model is a hot flocking model. The model has significant potential applications in biology, physics, control theory, computer science, etc. This project studies some problems related to the C-S flocking model under random interactions. We first investigate the C-S model with randomly limited communication ranges on general digraphs, at each time slice, each pair of neighboring agents can communicate with each other only when they are within some random communication range. Additionally, we study collision- avoiding C-S model subject to random failure with alternating rooted leaders, at each time step, there is a leader, but it can be switched among the agents from time to time, and there exists a positive minimal distance between agents. At last we study singular C-S model under random interactions, at each time step, each of the agents can fail to interact with any of its neighbors, and agents are collision avoiding, or the singular communication weight will tend to infinite. We will establish the convergence to flocking depending on initial conditions and system parameters by studying the above problems.