Distributed Adaptive Flocking Control for Large-Scale Multiagent Systems

This article presents a novel distributed flocking control method for large-scale multiagent systems (LS-MASs) operating in uncertain environments. When dealing with a massive number of flocking agents in uncertain environments, existing flocking methods encounter the problem of communication complexity and "Curse of dimensionality" caused by the exponential growth of agent interactions while solving PDE-based optimal flocking control for large-scale systems. The mean field game (MFG) method addresses this issue by transforming interactions among all agents into the interaction of each individual agent with average effects represented by a probability density function (pdf) of other agents. However, relying solely on a pdf term to consider other agents' states can result in inefficient flocking performance due to the absence of a proficient coordination mechanism encompassing all agents involved in flocking. To overcome these difficulties and achieve the desired flocking performance for LS-MASs, the agents are decomposed into a finite number of subgroups. Each subgroup comprises a leader and followers, and a hybrid game theory is developed to manage both inter- and intragroup interactions. The method incorporates a cooperative game that links leaders from different groups to formulate distributed flocking control, a Stackelberg game that teams up leaders and followers within the same group to extend collective flocking behavior, and an MFG for followers to address the challenges of LS-MASs. Furthermore, to achieve distributed adaptive flocking using the hybrid game structure, we propose a hierarchical actor-critic-mass-based reinforcement learning technique. This approach incorporates a multiactor-critic method for leaders and an actor-critic-mass algorithm for followers, enabling adaptive flocking control in a distributed manner for large-scale agents. Finally, numerical simulation including comparison study and Lyapunov analysis demonstrates the effectiveness of the developed method.