论文标题
线性二次平均野外社会系统的分布式控制与异质代理
Distributed Control of Linear Quadratic Mean Field Social Systems with Heterogeneous Agents
论文作者
论文摘要
在本文中，我们研究了直接方法的平均场线性二次控制系统的社会最优性，在该方法中，子系统是通过网络拓扑来通过单个动态和成本耦合的。引入图表以表示大型人口系统的网络拓扑，其中节点代表称为群集和边缘的亚群，代表通信关系。通过直接方法，我们首先在集中信息结构下寻求最佳控制器，该信息以一组向前的随机微分方程为特征。然后在RICCAT方程的帮助下获得反馈控制器。最后，我们设计了具有平均场近似值的分布式控制器，该控制器具有渐近社会最优性的属性。
In this paper, we study the social optimality for mean field linear quadratic control systems following the direct approach, where subsystems are coupled via individual dynamics and costs according to a network topology. A graph is introduced to represent the network topology of the large-population system, where nodes represent subpopulations called clusters and edges represent communication relationship. By the direct approach, we first seek the optimal controller under centralized information structure, which characterized by a set of forward-backward stochastic differential equations. Then the feedback controller is obtained with the help of Riccat equations. Finally, we design the distributed controller with mean field approximations, which has the property of asymptotically social optimality.
