Output-Only Identification and Spectral Monitoring of Coupled Feedback Networks with Known Time-Varying Actuation
Jihwan Woo
Abstract
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.
Read the AI summary and key takeaways for traders on WOBR Quant Research.