论文标题
使用主要代理的平均场类型控制系统的稳定性分析
Stability analysis of mean field type control system with major agent
论文作者
论文摘要
本文涉及对一个主要药物组成的对照系统的研究，当时代理数量倾向于无穷大，在极限情况下，许多相同的次要药物。为了研究限制系统，我们使用平均场方法。我们首先证明了由有限维度和平均场类型子系统组成的系统的运动的存在和独特性。本文的主要结果是运动W.R.T.的稳定性。动力学，初始数据和控件的扰动。为了说明一般理论，我们检查了Stackelberg游戏，领导者控制着主要代理，而追随者会影响未成年人。使用一般理论，我们显示了解决方案的存在。
The paper is concerned with the study of a control system consisting of one major agent and many identical minor agents in the limit case when the number of agents tends to infinity. To study the limiting system we use the mean field approach. We first prove the existence and uniqueness of the motion for such system consisting of finite dimensional and mean field type subsystems. The main result of the paper is the stability of the motion w.r.t. perturbations of dynamics, initial data and controls. To illustrate the general theory, we examine the Stackelberg game where the leader controls the major agent while the follower affects the minor agents. Using the general theory, we show the existence of a solution.
