Proceedings in Applied Mathematics and Mechanics (2014)
Himpe Christian and Ohlberger Mario
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By Himpe Christian, Leibner Tobias, Rave Stephan, and Saak Jens
Proceedings in Applied Mathematics and Mechanics (2017)
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.
Himpe C., Leibner T., Rave S., and Saak J. (2017) Fast Low-Rank Empirical Cross Gramians. Proceedings in Applied Mathematics and Mechanics, 17, 841--842.