论文标题
领导者追随者网络的最佳分布式控制：可扩展设计
Optimal Distributed Control for Leader-Follower Networks: A Scalable Design
论文作者
论文摘要
本文的重点是针对由一个领导者和许多关注者组成的多机构系统的最佳控制。假定每个代理的动力学是线性的，并且性能索引是领导者和追随者的状态和行动的二次函数。领导者和追随者都在动态和成本中耦合。领导者的状态和所有追随者（称为均值场）的国家的平均值是所有代理人的共同信息；但是，追随者的当地状态是私人信息，其他代理商未知。结果表明，最佳分布式控制策略是线性变化的，其计算复杂性与关注者的数量无关。可以以分布式的方式计算此策略，在此过程中，领导者需要求解一个Riccati方程以确定其最佳策略，而每个追随者都需要求解两个Riccati方程以获得其最佳策略。 随后将此结果扩展到了无限的地平线打折和未估计的成本功能的情况，其中最佳的分布式策略被证明是固定的。提供了一个数字示例，提供了100美元的关注者，以证明结果的功效。
The focus of this paper is directed towards optimal control of multi-agent systems consisting of one leader and a number of followers in the presence of noise. The dynamics of every agent is assumed to be linear, and the performance index is a quadratic function of the states and actions of the leader and followers. The leader and followers are coupled in both dynamics and cost. The state of the leader and the average of the states of all followers (called mean-field) are common information and known to all agents; however, the local state of the followers are private information and unknown to other agents. It is shown that the optimal distributed control strategy is linear time-varying, and its computational complexity is independent of the number of followers. This strategy can be computed in a distributed manner, where the leader needs to solve one Riccati equation to determine its optimal strategy while each follower needs to solve two Riccati equations to obtain its optimal strategy. This result is subsequently extended to the case of the infinite horizon discounted and undiscounted cost functions, where the optimal distributed strategy is shown to be stationary. A numerical example with $100$ followers is provided to demonstrate the efficacy of the results.
