This article investigates the optimal control problem with disturbance rejection for discrete-time multi-agent systems under cooperative and non-cooperative graphical games frameworks. Given the practical challenges of obtaining accurate models, Q-function-based policy iteration methods are proposed to seek the Nash equilibrium solution for the cooperative graphical game and the distributed minmax solution for the non-cooperative graphical game. To implement these methods online, two reinforcement learning frameworks are developed, an actor-disturber-critic structure for the cooperative graphical game and an actor-adversary-disturber-critic structure for the non-cooperative graphical game. The stability of the proposed methods is rigorously analyzed, and simulation results are provided to illustrate the effectiveness of the proposed methods.
@article{arxiv.2504.07547,
title = {Strategic learning for disturbance rejection in multi-agent systems: Nash and Minmax in graphical games},
author = {Xinyang Wang and Martin Guay and Shimin Wang and Hongwei Zhang},
journal= {arXiv preprint arXiv:2504.07547},
year = {2025}
}