Distributed adaptive Nash equilibrium seeking for games of heterogeneous high-order players over a directed graph

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-06-07 DOI:10.1016/j.automatica.2025.112296

Congcong Tian , Jie Mei , Kaixin Tian , Guangfu Ma

引用次数: 0

Abstract

This paper investigates the distributed Nash equilibrium (NE) seeking problem for non-cooperative games involving heterogeneous high-order players over a directed graph. We first address the NE seeking problem of heterogeneous high-order integrators by employing a state transformation method, which reduces the high-order integrators to single integrators. A distributed NE seeking strategy is proposed, incorporating position estimators, gradient descent and state feedback. Furthermore, for the case of heterogeneous high-order players with parametric uncertainties, we propose another distributed strategy based on the model reference adaptive NE seeking idea, where a linear high-order virtual player is designed for each player to track. Both strategies converge to NE asymptotically, avoiding the need to interact with high-order derivative information or rely on shared gains. Finally, numerical simulations are performed to verify the effectiveness of the proposed algorithms.

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有向图上异构高阶博弈的分布式自适应纳什均衡寻求

研究了有向图上异构高阶参与人非合作博弈的分布式纳什均衡寻求问题。本文首先采用状态变换方法解决了异构高阶积分器的NE查找问题，该方法将高阶积分器简化为单个积分器。提出了一种结合位置估计、梯度下降和状态反馈的分布式网元搜索策略。此外，对于具有参数不确定性的异构高阶玩家，我们提出了另一种基于模型参考自适应网元搜索思想的分布式策略，该策略设计了一个线性高阶虚拟玩家供每个玩家跟踪。这两种策略都渐近收敛于NE，避免了与高阶导数信息交互或依赖共享收益的需要。最后，通过数值仿真验证了算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.