标题： 基于事件触发控制的非合作双寡头博弈纳什均衡寻求 显示英文标题

标题： Nash Equilibrium Seeking for Noncooperative Duopoly Games via Event-Triggered Control

摘要： 本文提出了一种新颖的方法，用于在双寡头非合作博弈中实现局部稳定收敛到纳什均衡，该方法基于分布式事件触发控制方案。 所提出的方法采用极值搜索，通过正弦扰动信号来估计未知二次收益函数的梯度（一阶导数）。 这是首次将非合作博弈以无模型的方式结合事件触发方法进行处理。 每个玩家独立评估相应的当前状态变量与其最后广播值之间的偏差以更新玩家动作，同时在执行路径带宽有限的情况下保持控制性能，并仍保证闭环动态的稳定性。 特别是，通过时间缩放技术、李雅普诺夫直接法和不连续系统的平均理论进行稳定性分析。 我们量化了纳什均衡周围最终小残差集的大小，并在一个示例中数值地说明了理论结果。 显示英文摘要

摘要： This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal perturbation signals applied to estimate the Gradient (first derivative) of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion integrated with the event-triggered methodology. Each player evaluates independently the deviation between the corresponding current state variable and its last broadcasted value to update the player action, while they preserve control performance under limited bandwidth of the actuation paths and still guarantee stability for the closed-loop dynamics. In particular, the stability analysis is carried out using time-scaling technique, Lyapunov's direct method and averaging theory for discontinuous systems. We quantify the size of the ultimate small residual sets around the Nash equilibrium and illustrate the theoretical results numerically on an example.