Fixed-Time Nash Equilibrium Seeking in Time-Varying Networks
Fixed-Time Nash Equilibrium Seeking in Time-Varying Networks
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DOI：
10.1109/tac.2022.3168527
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发表时间：
2023-04
影响因子：
6.8
通讯作者：
J. Poveda;M. Krstić;T. Başar
中科院分区：
文献类型：
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作者：
J. Poveda;M. Krstić;T. Başar
在这篇文章中，我们介绍了一阶和零阶纳什均衡寻求动力学与固定时间和实际的固定时间收敛证书的非合作博弈有许多球员。一阶算法在有限时间内实现精确收敛到博弈的纳什均衡，该时间可以由一个独立于玩家行为初始条件的常数来限定上限。此外，这些固定的时间界限可以预先规定的算法的参数的适当调整下的系统设计者。当玩家只能获得他们的成本函数的测量，我们考虑一类分布式多时间尺度零阶无模型自适应动态，实现半实际的固定时间稳定性，定性地保持固定时间的界限的一阶动态的时间尺度分离的增加。此外，通过利用固定时间的输入状态稳定性的属性，获得了进一步的结果，其中一些球员实现不同的寻求动态的混合游戏。快速和慢速切换通信图也纳入使用工具从混合动力系统。我们考虑潜在的游戏，以及一般的非潜在的强单调游戏。数值例子说明了我们的结果。
In this article, we introduce first-order and zeroth-order Nash equilibrium seeking dynamics with fixed-time and practical fixed-time convergence certificates for noncooperative games having finitely many players. The first-order algorithms achieve exact convergence to the Nash equilibrium of the game in a finite time that can be additionally upper bounded by a constant that is independent of the initial conditions of the actions of the players. Moreover, these fixed-time bounds can be prescribed a priori by the system designer under an appropriate tuning of the parameters of the algorithms. When players have access only to measurements of their cost functions, we consider a class of distributed multitime scale zeroth-order model-free adaptive dynamics that achieve semiglobal practical fixed-time stability, qualitatively preserving the fixed-time bounds of the first-order dynamics as the time scale separation increases. Moreover, by leveraging the property of fixed-time input-to-state stability, further results are obtained for mixed games where some of the players implement different seeking dynamics. Fast and slow switching communication graphs are also incorporated using tools from hybrid systems. We consider potential games as well as general nonpotential strongly monotone games. Numerical examples illustrate our results.