Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems

Authors:
Serkan Gugercin;Rostyslav V. Polyuga;Christopher Beattie;Arjan Van Der Schaft
Affiliations:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA;ABN AMRO N.V. Bank, Gustav Mahlerlaan 10, 1082 PP (PAC HQ2015) Amsterdam, The Netherlands;Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2012

Citing 9
Cited 2

A new algorithm for L2 optimal model reduction

Automatica (Journal of IFAC)
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations

SIAM Journal on Scientific Computing
L2-Gain and Passivity Techniques in Nonlinear Control

L2-Gain and Passivity Techniques in Nonlinear Control
State-space truncation methods for parallel model reduction of large-scale systems

Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
Model Reduction of MIMO Systems via Tangential Interpolation

SIAM Journal on Matrix Analysis and Applications
Balanced Truncation Model Reduction for a Class of Descriptor Systems with Application to the Oseen Equations

SIAM Journal on Scientific Computing
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems

SIAM Journal on Matrix Analysis and Applications
h2-norm optimal model reduction for large scale discrete dynamical MIMO systems

Journal of Computational and Applied Mathematics
Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity

Automatica (Journal of IFAC)

On the ADI method for the Sylvester equation and the optimal-H2 points

Applied Numerical Mathematics
Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.15

Visualization

Abstract

Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop a framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced model is a rational (tangential) interpolant that retains the port-Hamiltonian structure; hence it remains passive. We introduce an H"2-inspired algorithm for effective choice of interpolation points and tangent directions and present several numerical examples illustrating its effectiveness.