标题： 受控领导者-跟随者系统的微观-宏观和宏观-宏观极限 显示英文标题

标题： Micro-macro and macro-macro limits for controlled leader-follower systems

摘要： 我们研究一个受反馈控制的交互粒子领导者-跟随者系统，并通过两步传递过程推导其平均场极限：首先将其转化为耦合领导者粒子与跟随者流体的微观-宏观系统，然后进一步转化为完全连续的宏观-宏观系统。 对于每种极限过程，我们基于调制能量方法和Wasserstein距离建立了定量稳定性与收敛性估计。 这些结果为受控多智能体系统的分层约简提供了严格的理论基础。 给出了数值模拟，包括超出所考虑解析类别的相互作用势的例子，以展示动态行为并支持理论结果。 显示英文摘要

摘要： We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a fully continuum macro-macro system. For each limiting procedure, we establish quantitative stability and convergence estimates based on modulated energy methods and Wasserstein distances. These results provide a rigorous foundation for the hierarchical reduction of controlled multi-agent systems. Numerical simulations are presented, including examples with interaction potentials beyond the analytical class considered, to demonstrate the dynamics and support the theoretical results.