@article{Lian2025, 
author = {Bosen Lian and Nhan T. Nguyen and Frank L. Lewis},
title = {Distributed Cluster Containment Control of Swarms via Differential Game-Theoretic Learning},
year = {2025},
journal = {Unmanned Systems},
volume = {13},
number = {5},
pages = {1283-1294},
keywords = {reinforcement learning, distributed control, Swarm, graphical differential game},
url = {https://www.sciopen.com/article/10.1142/S2301385025440017},
doi = {10.1142/S2301385025440017},
abstract = {This paper addresses the cluster containment control problem for a swarm of linear unmanned systems operating over a directed communication graph and subject to external disturbances, formulating it as a graphical differential game. Each agent independently computes a distributed optimal control strategy using only local information, ensuring both cluster containment and Nash equilibrium behavior within the game framework, while also maintaining robustness to external disturbances. The closed-loop system is proven to be asymptotically stable, and the existence of a Nash-minmax solution for each agent is established. To implement the control strategy without requiring a model of the system dynamics, a model-free, data-driven reinforcement learning algorithm is proposed for the online computation of distributed Nash-minmax control policies, accompanied by convergence guarantees. The effectiveness of the proposed framework is demonstrated through simulations involving swarms of unmanned aerial vehicles and unmanned ground vehicles.}
}