Proper Orthogonal Decomposition for Model Reduction of Linear Differential-Algebraic Equation Systems

摘要

This paper presents a generalization of the model reduction method proper orthogonal decomposition to systems of differential-algebraic equations of arbitrary index. It is known that proper orthogonal decomposition generalizes the method of empirical balanced truncation for linear time-invariant systems. This property will be preserved for differential-algebraic equation systems of arbitrary index. This is important for the application of proper orthogonal decomposition in control, where the input-output behaviour should be approximated accurately, which is a well-known property of balanced-truncated systems.