Data-Driven Model Reduction by Moment Matching for Linear Systems Driven by an Unknown Implicit Signal Generator

We study the model reduction by moment matching problem for linear systems in a data-driven framework. We show that reduced-order models can be directly computed from data without knowledge of the structure of the signal generator or of its internal state. The reduced-order models thus obtained match the moments of the unknown underlying system asymptotically. Our construction provides a simple way to enforce additional constraints in the reduced-order model. We demonstrate the applicability of the results using data from a high-dimensional model of a building.