Momentum-Based Nash Set-Seeking Over Networks Via Multi-Time Scale Hybrid Dynamic Inclusions
Momentum-Based Nash Set-Seeking Over Networks Via Multi-Time Scale Hybrid Dynamic Inclusions
复制标题
DOI：
10.1109/tac.2023.3321901
复制
发表时间：
2021-10
影响因子：
6.8
通讯作者：
Daniel E. Ochoa;J. Poveda
中科院分区：
文献类型：
--
作者：
Daniel E. Ochoa;J. Poveda
多时间尺度技术，如奇异摄动和平均理论，在网络系统分布式纳什均衡寻求算法的发展中发挥了重要作用。这种技术依赖于在闭环系统的每个时间尺度上演化的动力学的一致渐近稳定性。当这些性质不存在时，多时间尺度纳什均衡寻求算法的综合更具挑战性，需要额外的正则化机制。在本文中，我们研究了在非合作对策中具有时变阻尼的加速伪梯度流背景下这些机制的综合和分析。具体来说，我们介绍了一类新的分布式和混合纳什集搜索算法，它将基于动量的动态流与协调的离散时间重置协同结合起来。重置机制可以被看作是一种重新启动技术，它允许个体玩家选择自己的动量重新启动策略，从而获得更好的瞬时性能。将得到的闭环系统建模为混合动力包含，并利用混合动力系统理论的工具对其进行了分析。我们的算法是为潜在游戏开发的，也为不存在潜在函数的单调游戏开发的。它们可以在玩家可以访问带有多代理系统全部或部分信息的梯度预言机的游戏中执行，也可以在玩家只能访问成本测量的游戏中执行。在后一种情况下，我们使用混合极值寻求控制的工具。
Multitime scale techniques, such as singular perturbations and averaging theory, have played an important role in the development of distributed Nash equilibrium seeking algorithms for network systems. Such techniques rely on the uniform asymptotic stability properties of the dynamics that evolve in each of the time scales of the closed-loop system. When such properties are absent, the synthesis of multitime scale Nash equilibrium-seeking algorithms is more challenging and it requires additional regularization mechanisms. In this article, we investigate the synthesis and analysis of these mechanisms in the context of accelerated pseudogradient flows with time-varying damping in noncooperative games. Specifically, we introduce a new class of distributed and hybrid Nash set-seeking algorithms that synergistically combine dynamic momentum-based flows with coordinated discrete-time resets. The reset mechanisms can be seen as restarting techniques that allow individual players to choose their own momentum restarting policy to potentially achieve better transient performance. The resulting closed-loop system is modeled as a hybrid dynamic inclusion, which is analyzed using tools from hybrid dynamical system's theory. Our algorithms are developed for potential games, as well as for monotone games for which a potential function does not exist. They can be implemented in games where players have access to gradient Oracles with full or partial information of the multiagent system, as well as in games where players have access only to measurements of their costs. In the latter case, we use tools from hybrid extremum seeking control.