This paper addresses a nonsmooth aggregative game to control multiple noncooperative players, each with a nonsmooth cost function that depends not only on its own decision but also on some aggregate effect among all the agents. In addition, the decision of each player is restricted by private and coupling constraints. To address these concerns, a distributed generalized Nash equilibrium (GNE) seeking algorithm is proposed. Two features distinguish our methods from the existing GNE seeking algorithms. Firstly, an adaptive penalty method is introduced to drive each player’s action to enter the set of private constraints. The adaptive term ensures automatic adjustment of penalty parameter based on the degree of constraint violation excluding any prior calculation. Secondly, a distributed dynamic event-triggered mechanism is designed for each player to lessen communication energy. In comparison to the static event-triggered mechanism, the proposed dynamic mechanism possesses larger inter-execution time intervals. As the discontinuity of the event-triggered mechanism can impact the existence of a solution to the closed-loop system in the classical sense, we adapt a nonsmooth analysis technique, including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, the convergence result and the avoidance of Zeno behavior are established. Finally, two engineering examples are provided to demonstrate the validity of the theoretical results.

中文翻译：

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动态事件触发机制下非光滑聚合博弈的自适应广义纳什均衡寻求算法


本文提出了一种控制多个非合作参与者的非平滑聚合博弈，每个参与者都有一个非平滑成本函数，该函数不仅取决于自己的决策，还取决于所有代理之间的某种聚合效应。此外，每个参与者的决策都受到私人和耦合约束的限制。为了解决这些问题，提出了一种分布式广义纳什均衡（GNE）搜索算法。我们的方法有两个特点与现有的 GNE 搜索算法不同。首先，引入自适应惩罚方法来驱动每个玩家的动作进入私人约束集。自适应项确保根据约束违反程度自动调整惩罚参数，排除任何先前的计算。其次，为每个玩家设计了分布式动态事件触发机制，以减少通信能量。与静态事件触发机制相比，所提出的动态机制具有更大的执行间时间间隔。由于事件触发机制的不连续性会影响经典意义上闭环系统解的存在性，因此我们采用了非光滑分析技术，包括微分包含和 Filippov 解。通过非光滑李亚普诺夫分析，建立了收敛结果和避免芝诺行为的方法。最后通过两个工程实例验证了理论结果的有效性。