AI 中文总结
研究仅用零阶信息的随机多智能体系统分布式时变优化，构建慢-快随机框架，引入辅助变量和快速子系统生成梯度估计，慢子系统进行优化和一致性，分析收敛性并通过模拟验证，建立界表征参数等对跟踪性能的影响。
AI 中文摘要
本文研究仅使用零阶信息的随机多智能体系统（SMASs）的分布式时变优化。与现有在单个时间尺度上直接耦合梯度估计和优化更新的方法不同，本文通过引入辅助快速系统构建了一个新颖的随机奇异摄动框架。该方案自然形成慢-快耦合结构，通过引入辅助变量和构建快速子系统生成平滑梯度估计，而智能体状态演化作为慢子系统进行分布式优化和一致性。利用随机奇异摄动技术和随机李雅普诺夫理论分析了该方案的收敛性。结果表明，快速子系统迅速收敛到瞬时随机梯度估计，慢子系统以概率实现实际固定时间一致性（Pfxc）并渐近有界地跟踪时变最优轨迹。此外，本文建立了明确的界来表征参数、随机干扰和目标函数性质对跟踪性能的影响。最后，通过数值模拟验证了理论结果。
英文摘要
This paper investigates the distributed time-varying optimization of stochastic multi-agent systems (SMASs) using only zero-order information. Unlike existing methods that directly couple gradient estimation and optimization updates on a single time scale, this paper constructs a novel stochastic singular perturbation framework by introducing auxiliary fast systems. The proposed scheme naturally forms a slow-fast coupling structure: by introducing auxiliary variables and constructing fast subsystems to generate smooth gradient estimates, while the agent's state evolution, as the slow subsystem, performs distributed optimization and consensus. The convergence of the proposed scheme is analyzed using stochastic singular perturbation techniques and stochastic Lyapunov theory. The results show that the fast subsystem converges rapidly to the instantaneous stochastic gradient estimates, while the slow subsystem achieves practically fixed-time consensus (Pfxc) in probability and asymptotically bounded tracks the time-varying optimal trajectory. Furthermore, this paper establishes explicit bounds to characterize the effects of parameters, stochastic disturbances, and the properties of the objective function on tracking performance. Finally, the theoretical results are validated through numerical simulations.
