论文标题
领导者的社会最佳选择均值字段线性二次控制
Social Optima in Leader-Follower Mean Field Linear Quadratic Control
论文作者
论文摘要
本文调查了线性二次平均野外领导者团队问题，该模型涉及一个领导者和大量弱耦合的交互式关注者。领导者和追随者合作优化社会成本。具体而言，对于领导者首先提供的任何策略，追随者希望选择一种策略来最大程度地减少社会成本功能。使用变分分析和人为最佳性，我们构建了两个辅助控制问题。通过依次解决具有一致平均场近似值的辅助控制问题，我们可以通过一类前回头的一致性系统来获得一组分散的社会最佳策略。在某些适当的条件下，相关的Stackelberg平衡进一步证明。
This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. The leader and the followers cooperate to optimize the social cost. Specifically, for any strategy provided first by the leader, the followers would like to choose a strategy to minimize social cost functional. Using variational analysis and person-by-person optimality, we construct two auxiliary control problems. By solving sequentially the auxiliary control problems with consistent mean field approximations, we can obtain a set of decentralized social optimality strategy with help of a class of forward-backward consistency systems. The relevant Stackelberg equilibrium is further proved under some proper conditions.
