论文标题
平均字段线性二次控制：统一稳定和社会最优性
Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimality
论文作者
论文摘要
本文涉及一般平均线性二次控制系统的统一稳定和社会最优性，在该系统中，子系统是通过单个动力学和成本耦合的，并且在确定性条件下不假定状态重量。对于有限摩托问题，我们首先从变异分析中获得一组向前的随机微分方程（FBSDE），并通过解耦FBSDE来构建反馈类型控制。对于无限 - 摩尼子问题，通过使用两个Riccati方程的解决方案，我们设计了一套分散的控制定律，这进一步被证明是渐近的社会最佳选择。在不同情况下分别给出了一些等效条件，以均匀地稳定系统。最后，将提出的分散对照与以前的作品中的渐近最佳策略进行了比较。
This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the definiteness condition. For the finite-horizon problem, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems in different cases, respectively. Finally, the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works.
