This article explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on the internal model are proposed for the case with perfect and imperfect information, respectively. Different from the existing algorithms based on gradient dynamics, by introducing the integral of the gradient of cost functions on the basis of the passivity theory, the rules are proposed to force the strategies of all agents to evolve to the Nash equilibrium, regardless of the effect of disturbances. The convergence of the two strategy-updating rules is analyzed via the Lyapunov stability theory, passivity theory, and singular perturbation theory. Simulations are performed to illustrate the effectiveness of the proposed methods.

中文翻译：

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具有抗扰性的一般线性系统的纳什均衡求解


本文探讨了受外部干扰的一般线性系统网络中的聚合博弈。为了应对外部干扰，针对完全信息和不完全信息的情况，分别提出了基于内部模型的分布式策略更新规则。与现有基于梯度动力学的算法不同，通过在被动性理论的基础上引入成本函数梯度的积分，提出规则迫使所有智能体的策略向纳什均衡演化，而不管效果如何的干扰。通过Lyapunov稳定性理论、被动性理论和奇异摄动理论分析了两种策略更新规则的收敛性。进行仿真以说明所提出方法的有效性。