System Reduction Using an LQR-Inspired Version of Optimal Replacement Variables (Communications in Computational Physics, 2012)
Optimal Replacement Variables (ORV) is a method for approximating a largesystem of ODEs by one with fewer equations, while attempting to preserve the essential dynamics of a reduced set of variables of interest. An earlier version of ORV [1]had some issues, including limited accuracy and in some rare cases, instability. Herewe present a new version of ORV, inspired by the linear quadratic regulator problem ofcontrol theory, which provides better accuracy, a guarantee of stability and is in someways easier to use.