Stability-Preserving, Adaptive Model Order Reduction of DAEs by Krylov-Subspace Methods
For engineers and scientists working with large-scale DAE systems, this work provides stability-preserving reduction techniques that maintain algebraic constraints, though it is an incremental extension of existing Krylov-subspace methods.
This paper addresses model order reduction for high-order differential-algebraic equations (DAEs) from constrained mechanical systems and electrical networks. It presents two stability-preserving methods: one preserving strict dissipativity and another using H2-pseudo-optimal reduction with adaptive selection of reduced order and Krylov shifts.
Systems of differential-algebraic equations (DAEs) represent a widespread formalism in the modeling of constrained mechanical systems and electrical networks. Due to the automatic, object-oriented generation of the equations of motion and the resulting redundancies in the descriptor variables, DAE systems often reach a very high order. This motivates the use of model order reduction (MOR) techniques that capture the relevant input-output dynamics in a reduced model of much smaller order, while satisfying the constraints and preserving fundamental properties. Due to their particular structure, new MOR techniques designed to work directly on the DAE are required that reduce the dynamical part while preserving the algebraic. In this contribution, we exploit the specific structure of index-1 systems in semi-explicit form and present two different methods for stability-preserving MOR of DAEs. The first technique preserves strictly dissipativity of the underlying dynamics, the second takes advantage of H2-pseudo-optimal reduction and further allows for an adaptive selection of reduction parameters such as reduced order and Krylov shifts.