Hierarchical game theoretical distributed adaptive control for large scale multi‐group multi‐agent system

Abstract

Abstract This paper introduces a distributed adaptive formation control for large‐scale multi‐agent systems (LS‐MAS) that addresses the heavy computational complexity and communication traffic challenges while directly extending conventional distributed control from small scale to large scale. Specifically, a novel hierarchical game theoretic algorithm is developed to provide a feasible theory foundation for solving LS‐MAS distributed optimal formation problem by effectively integrating the mean‐field game (MFG), the Stackelberg game, and the cooperative game. In particular, LS‐MAS is divided into multiple groups geographically with each having one group leader and a significant amount of followers. Then, a cooperative game is used among multi‐group leaders to formulate distributed inter‐group formation control for leaders. Meanwhile, an MFG is adopted for a large number of intra‐group followers to achieve the collective intra‐group formation while a Stackelberg game is connecting the followers with their corresponding leader within the same group to achieve the overall LS‐MAS multi‐group formation behavior. Moreover, a hybrid actor–critic‐based reinforcement learning algorithm is constructed to learn the solution of the hierarchical game‐based optimal distributed formation control. Finally, to show the effectiveness of the presented schemes, numerical simulations and Lyapunov analysis is performed.

Keywords

• Formation control
• Game theory
• Large‐scale systems
• Multi‐agent systems
• Neural nets
• Optimal control