Signal Generator Agnostic Moment Matching

We study the model-reduction problem by moment matching for linear and nonlinear systems in a data-driven setting. We show that reduced-order models can be directly computed from input–output data without requiring knowledge of the structure of the signal generator or its internal state. The reduced-order models thus obtained match the moments of the unknown underlying system asymptotically. Our formulation provides a simple way to enforce additional constraints on the structure of the reduced-order model, which could be used to incorporate prior knowledge about the underlying system. In addition, we show that our method can be directly applied to a large class of linear and nonlinear time-delay systems with minimal modifications. Finally, we provide a simple algorithmic formulation that can be used directly with data, and demonstrate its effectiveness on a benchmark example—a nonlinear RC ladder circuit.