System Reduction Using an LQR-Inspired Version of Optimal Replacement Variables

Optimal ReplacementVariables(ORV)is amethod for approximating a large system 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.Here we present a newversion of ORV,inspired by the linear quadratic regulator problemof control theory,which provides better accuracy,a guarantee of stability and is in some ways easier to use.