An aggregative game involving double-integrator agents is investigated. In this game, the dynamics of all players are subjected to unknown time-varying disturbances and unmodeled terms, and are also influenced by networked attacks on the communication topology. To seek a Nash equilibrium for such games, a novel distributed robust Nash equilibrium seeking algorithm is proposed and the complete closed-loop system is modeled as a hybrid system using an average dwell-time automaton and a time-ratio monitor to constrain attacks. Then, to analyze stability for the proposed algorithm, a Lyapunov function is constructed and uniform asymptotic stability is obtained under a local Lipschitz assumption on the gradients of the payoff functions. In addition, global uniform asymptotic stability is obtained under a global Lipschitz assumption on the gradients. Finally, an example is used to illustrate the results.

研究了涉及双重整合者的综合博弈。在此游戏中，所有玩家的动态都会受到未知的时变干扰和非模型项的影响，并且还受到对通信拓扑结构的网络攻击的影响。为了寻求此类游戏的Nash平衡，提出了一种新颖的分布式鲁棒Nash平衡搜索算法，并将完整的闭环系统建模为使用平均停留时间自动机和时间比率监视器约束攻击的混合系统。然后，为分析所提出算法的稳定性，构造了一个Lyapunov函数，并在局部Lipschitz假设下在收益函数的梯度上获得了一致的渐近稳定性。另外，在梯度的全局Lipschitz假设下获得了全局一致的渐近稳定性。