论文标题

领导者追随者网络中的近乎最佳控制策略:线性二次平均场团队的案例研究

Near-Optimal Control Strategy in Leader-Follower Networks: A Case Study for Linear Quadratic Mean-Field Teams

论文作者

Baharloo, Mohammad M., Arabneydi, Jalal, Aghdam, Amir G.

论文摘要

在本文中,研究了一个由一个领导者组成的分散随机控制系统,并研究了许多同质追随者。领导者和追随者都在动态和成本中耦合在一起,在这种动态和成本中,在领导者和追随者的状态和行动中,成本函数是二次的。领导者和追随者的目标是达成共识,同时最大程度地减少他们的沟通和能源成本。领导者知道其地方国家,每个追随者都知道其地方国家和领导状态。实现此分散信息结构所需链接的数量等于关注者的数量,这是要连接通信图的最小链接数。在没有领导者的特殊情况下,关注者之间无需链接,即,通信图甚至没有连接。我们提出了一种近乎最佳的控制策略,随着追随者的数量增加,该策略会收敛到最佳解决方案。提出的解决方案的显着特征之一是它提供了一个设计方案,在该方案中,可以通过选择适当的成本功能来设计关注者的集体行为。另外,提出的解决方案的计算复杂性不取决于关注者的数量。此外,可以以分布式方式计算提出的策略,在此过程中,领导者求解一个riccati方程,每个追随者都求解两个riccati方程来计算其策略。提供了两个数值示例,以证明结果在控制多代理系统中的有效性。

In this paper, a decentralized stochastic control system consisting of one leader and many homogeneous followers is studied. The leader and followers are coupled in both dynamics and cost, where the dynamics are linear and the cost function is quadratic in the states and actions of the leader and followers. The objective of the leader and followers is to reach consensus while minimizing their communication and energy costs. The leader knows its local state and each follower knows its local state and the state of the leader. The number of required links to implement this decentralized information structure is equal to the number of followers, which is the minimum number of links for a communication graph to be connected. In the special case of leaderless, no link is required among followers, i.e., the communication graph is not even connected. We propose a near-optimal control strategy that converges to the optimal solution as the number of followers increases. One of the salient features of the proposed solution is that it provides a design scheme, where the convergence rate \edit{as well as} the collective behavior of the followers can be designed by choosing appropriate cost functions. In addition, the computational complexity of the proposed solution does not depend on the number of followers. Furthermore, the proposed strategy can be computed in a distributed manner, where the leader solves one Riccati equation and each follower solves two Riccati equations to calculate their strategies. Two numerical examples are provided to demonstrate the effectiveness of the results in the control of multi-agent systems.

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