Fast Low-Rank Empirical Cross Gramians

The cross Gramian matrix encodes the input‐output coherence of linear control systems and is used in projection‐based model reduction. The empirical cross Gramian is a data‐driven variant of the cross Gramian which also extends to nonlinear systems. A drawback of the empirical cross Gramian for large‐scale systems is its full order and dense structure; yet, it may be computed column‐wise. Using the hierarchical approximate proper orthogonal decomposition (HAPOD), this partial computability can be exploited to obtain a truncated projection for model order reduction without assembling a full cross Gramian. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)