Data-driven modeling with prior system knowledge

The behavior of a linear time-invariant system can be characterized entirely by measured input–output data that spans the vector space of all possible trajectories of the system relying on the fundamental lemma by Willems et al. However, useful a priori knowledge of the system is usually neglected. We propose a novel method for incorporating prior knowledge, specifically, known pole and zero locations, into a data-driven representation by constructing filters that pre-process the measured input–output data. To this end, a physics-informed data-driven predictor is introduced, where trajectories are obtained as linear combinations of the columns of a filtered block-Hankel matrix. We explicitly derive the output prediction error and show how leveraging prior knowledge reduces the impact of future noise realizations on output predictions and improves the accuracy of the initial state that is inferred from past data.