In this paper, we investigate a prescribed-time and fully distributed Nash Equilibrium (NE) seeking problem for continuous-time noncooperative games. By exploiting pseudo-gradient play and consensus-based schemes, various distributed NE seeking algorithms are presented over either fixed or switching communication topologies so that the convergence to the NE is reached in a prescribed time. In particular, a prescribed-time distributed NE seeking algorithm is firstly developed under a fixed graph to find the NE in a prior-given and user-defined time, provided that a static controller gain can be selected based on certain global information such as the algebraic connectivity of the communication graph and both the Lipschitz and monotone constants of the pseudo-gradient associated with players' objective functions. Secondly, a prescribed-time and fully distributed NE seeking algorithm is proposed to remove global information by designing heterogeneous dynamic gains that turn on-line the weights of the communication topology. Further, we extend this algorithm to accommodate jointly switching topologies. It is theoretically proved that the global convergence of those proposed algorithms to the NE is rigorously guaranteed in a prescribed time based on a time function transformation approach. In the last, numerical simulation results are presented to verify the effectiveness of the designs.

中文翻译：

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非合作博弈中的规定时间完全分布纳什均衡寻求

在本文中，我们研究了连续时间非合作博弈的规定时间和完全分布式纳什均衡 (NE) 寻求问题。通过利用伪梯度播放和基于共识的方案，在固定或交换通信拓扑上提出了各种分布式 NE 搜索算法，以便在规定的时间内达到 NE 的收敛。具体而言，首先在固定图下开发了一种规定时间分布式NE寻找算法，以在先验给定和用户定义的时间内找到NE，前提是可以根据某些全局信息选择静态控制器增益，例如通信图的代数连通性以及与玩家目标函数相关的伪梯度的 Lipschitz 和单调常数。第二，提出了一种规定时间和完全分布式的 NE 搜索算法，通过设计异构动态增益来去除全局信息，该增益使通信拓扑的权重在线。此外，我们扩展了该算法以适应联合切换拓扑。理论上证明，基于时间函数变换方法，这些算法在规定时间内严格保证全局收敛到NE。最后通过数值模拟结果验证了设计的有效性。理论上证明，基于时间函数变换方法，这些算法在规定时间内严格保证全局收敛到NE。最后通过数值模拟结果验证了设计的有效性。理论上证明，基于时间函数变换方法，这些算法在规定时间内严格保证全局收敛到NE。最后通过数值模拟结果验证了设计的有效性。