2022/06/08 by Moser, Tim, Schwerdtner, Paul, Mehrmann, Volker +1
#Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2206.03942
We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to represent any linear time-invariant pH-DAE with a minimal number of parameters, which makes it well-suited to model reduction. We propose two algorithms which directly optimize the parameters of a reduced model to approximate a given large-scale model with respect to either the H-infinity or the H-2 norm. This approach has several benefits. Our parameterization ensures that the reduced model is again a pH-DAE system and enables a compact representation of the algebraic part of the large-scale model, which in projection-based methods often requires a more involved treatment. The direct optimization is entirely based on transfer function evaluations of the large-scale model and is therefore independent of the system matrices' structure. Numerical experiments are conducted to illustrate the high accuracy and small reduced model orders in comparison to other structure-preserving MOR methods.