Distributed Nash Equilibrium Seeking in Aggregative Games Over Jointly Connected and Weight-Balanced Networks

• 成果类型: Article
• 署名作者: Liu, Zhaocong; Huang, Jie
• 署名单位: Chinese University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3520809
• 发表日期: 2025
• 页码: 3486-3493
• 关键词: games; Nash equilibrium; switches; vectors; cost function; communication networks; Aggregates; STABILITY; Jacobian matrices; control theory; Aggregative games; converse Lyapunov theorem; exponential stability; jointly connected networks

摘要

The problem of the distributed Nash equilibrium (NE) seeking for aggregative games has been studied over strongly connected and weight-balanced static networks and every time strongly connected and weight-balanced switching networks. In this article, we further study the same problem over jointly connected and weight-balanced networks. The existing approaches critically rely on the connectedness of the network and these approaches fail if the network is not connected. To overcome this difficulty, we propose a novel approach to showing the exponential convergence of the output of the closed-loop system to the unknown NE point under a set of mild conditions. For this purpose, we need to establish the exponential stability for a time-varying ancillary system. By the converse Lyapunov theorem, this result guarantees the existence of a time-varying quadratic Lyapunov function for the ancillary system, which in turn leads to the construction of a suitable Lyapunov function for the closed-loop system, thus leading to the solution of the problem. A numerical example is presented to validate the effectiveness of our distributed algorithm.