Model Reduction via Proper Orthogonal Decomposition

Abstract

In this lecture notes an introduction to model reduction utilizing proper orthogonal decomposition (POD) is given. The close connection be- tween POD and singular value decomposition (SVD) of rectangular matrices is emphasized. As an application PODis used to derive a reduced-ordermodel for non-linear initial value problems. The strategy is extended to linear-quadratic optimal control problems governed by ordinary differential equations. The re- lationship to classical model reduction techniques like balanced truncation is studied. 1.