This article studies the tracking control problem with a large-scale group of agents. Unlike traditional control techniques used in multiagent systems (MASs), a new type of intelligent design is needed to handle the intractable “Curse of Dimensionality” caused by the extremely large number of agents. To address this challenge, the mean field game (MFG) theory has been embedded into reinforcement learning to advance intelligent tracking control with large-scale MAS. Specifically, MFG-based control can calculate the optimal strategy based on one unified fix-dimension probability density function (pdf) instead of high-dimensional large-scale MAS information collected from individual agents. Moreover, the approximate dynamic programming technique is adopted to generate a new type of MFG-based algorithm. Each agent has three neural networks (NNs) to approximate the solution of the mean field type control. In addition to the algorithm development, the performance of the NNs is also analyzed using the Lyapunov method. Finally, the linear and nonlinear tracking control simulations are given to evaluate the algorithm’s performance.

中文翻译：

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使用平均场游戏的大规模多智能体系统跟踪控制

本文研究了大规模代理组的跟踪控制问题。与多智能体系统（MAS）中使用的传统控制技术不同，需要一种新型的智能设计来处理由大量智能体引起的棘手的“维度诅咒”。为了应对这一挑战，平均场博弈 (MFG) 理论已被嵌入到强化学习中，以通过大规模 MAS 推进智能跟踪控制。具体来说，基于 MFG 的控制可以基于一个统一的固定维概率密度函数 (pdf) 来计算最优策略，而不是从单个代理收集的高维大规模 MAS 信息。此外，采用近似动态规划技术生成了一种新型的基于MFG的算法。每个代理都有三个神经网络（NN）来近似平均场类型控制的解决方案。除了算法开发之外，还使用 ​​Lyapunov 方法分析了 NN 的性能。最后，给出了线性和非线性跟踪控制仿真来评估算法的性能。