发表机构
School of Mechano-electronic Engineering, Xidian University; School of Control and Computer Engineering, North China Electric Power University（西安电子科技大学机电工程学院; 华北电力大学控制与计算机工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对开放多联盟网络中智能体动态进出导致的梯度信息丢失问题，提出质量保持的梯度跟踪算法，实现分布式纳什均衡寻求，并设计指数间隔递减步长加速收敛，仿真验证有效性。
AI 中文摘要
本文研究了开放多联盟网络中的分布式信息聚合与纳什均衡寻求问题，其中智能体和联盟都可能动态地进入或离开网络。网络人口的变化对传统的梯度跟踪方法构成了根本性挑战，因为智能体的离开可能导致分布式聚合所需的梯度信息丢失。为克服这一问题，设计了一种质量保持的梯度跟踪方法，其中离开智能体所携带的梯度信息被重新分配给同一联盟内的剩余智能体。所提出的方法在联盟内部通信网络上保持了联盟目标的聚合梯度信息，并在动态人口变化下实现了梯度跟踪，且无需在传统梯度跟踪方法之外施加额外的初始化条件。基于所提出的梯度跟踪机制，开发了一个分布式纳什均衡寻求框架，并在非协调的固定步长和递减步长下建立了其收敛性。此外，为了缓解经典递减步长方案（$\frac{\eta_0}{t}$，其中$\eta_0>0$为常数）导致的收敛速度减慢，基于智能体的探索区间设计了一种指数间隔递减步长方案。最后，基于开放连接控制博弈的数值仿真验证了所提出的信息跟踪与纳什均衡寻求框架的有效性。
英文摘要
This paper studies distributed information aggregation and Nash equilibrium seeking over open multi-coalition networks, where both agents and coalitions may dynamically enter and leave the network. The varying network population poses a fundamental challenge to conventional gradient-tracking methods, as agent departures may cause the loss of gradient information required for distributed aggregation. To overcome this issue, a mass-preserving gradient-tracking method is designed, in which the gradient information carried by departing agents is redistributed to the remaining agents within the same coalition. The proposed method preserves the aggregate gradient information of the coalition objective over the intra-coalition communication network and achieves gradient tracking under dynamic population changes without imposing additional initialization conditions beyond those of conventional gradient-tracking methods. Based on the proposed gradient-tracking mechanism, a distributed Nash equilibrium seeking framework is developed, and its convergence is established under both uncoordinated fixed and diminishing stepsizes. Furthermore, to alleviate the slowdown of convergence caused by classical diminishing stepsize schemes ($\frac{η_0}{t}$, where $η_0>0$ is a constant), an exponential-interval diminishing stepsize scheme is designed based on the agents' exploration intervals. Finally, a numerical simulation based on an open connecting control game demonstrate the effectiveness of the proposed information-tracking and Nash equilibrium seeking framework.
Comments13 pages, 5 figures
