仅输出型耦合反馈网络的识别与频谱监测（含已知时变驱动）
Output-Only Identification and Spectral Monitoring of Coupled Feedback Networks with Known Time-Varying Actuation
- Amazon Web Services（亚马逊云科技）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对仅输出场景下含已知时变驱动的耦合反馈网络，提出基于结构特征的识别方法，经仿真与真实杠杆基金数据验证，可实现耦合识别与频谱监测。
AI中文摘要：
耦合反馈网络通常按通道逐一监测，尽管跨通道路径会改变稳定裕度与传输的扰动。我们研究在仅输出场景下结构化反馈矩阵 L_t = Φ diag(γ_t) 的识别：不存在指令、探测或参考输入，仅观测到时间上分离的输出与调度增益 γ_t，而耦合响应 Φ 与清算窗口输入则不可观测。识别依赖于观测到的窗口前输出的持续激励，以及两项将耦合与混淆项区分开的结构特征：增益的已知时变特性，其以可预测模式调制闭环响应；以及部分反转时刻，即后续窗口中校正了暂态位移的已知比例。我们给出一系列结果：在增益 regime 的雅可比秩条件下实现耦合的精确局部识别；一阶交互估计器，其识别强度为残差交互信息矩阵的最小特征值（在恒定增益下可证无法识别）；将被估计量表征为预解灵敏度——该对象适用于筛选传输扰动，亦是频谱裕度恢复的第一阶段输入，一阶估计器具有√T渐近性，交叉识别定理将每个时变增益映射至恰好可识别的预解行与列，且在一致选择下具有自助法有效性；所实现启发式方法的经验覆盖率（名义95%下为90%）量化了剩余差距。仿真验证了秩条件的尖锐性，并量化了存在混淆时的基准失效情况。对杠杆基金再平衡反馈的案例研究中，每日基金披露数据充当已知增益，用真实数据说明了该方法的有效性。
英文摘要：
Coupled feedback networks are often monitored channel by channel even though cross-channel paths alter both stability margins and transmitted disturbances. We study identification of a structured feedback matrix L_t = Phi diag(gamma_t) in an output-only setting: no commanded, probing, or reference input exists -- only temporally separated outputs and the scheduling gains gamma_t are observed, while the coupling response Phi and the clearing-window inputs are not. Identification rests jointly on the persistent excitation of the observed pre-window output and on two structural features separating coupling from confounds: the known time variation of the gains, which modulates the closed-loop response in a predictable pattern, and a partial-reversal moment by which a known fraction of transient displacement is corrected in a subsequent window. We give a hierarchy of results: exact local identification of the coupling under a Jacobian rank condition on the gain regimes; a first-order interaction estimator whose identification strength is the minimum eigenvalue of the residualized interaction information matrix (provably unidentified under constant gains); and a characterization of the estimand as a resolvent sensitivity -- the right object for screening transmitted disturbances and a first-stage input to spectral-margin recovery -- with sqrt(T) asymptotics for the first-order estimator, a cross-identification theorem mapping each varying gain to exactly identified resolvent rows and columns, and bootstrap validity under consistent selection; the implemented heuristic's empirical coverage (90% at nominal 95%) quantifies the remaining gap. Simulations verify sharpness of the rank condition and quantify benchmark failures under confounding. A case study on leveraged-fund rebalancing feedback, where daily fund disclosures play the role of the known gains, illustrates the method on real data.
