Structure-preserving model reduction on manifolds of port-Hamiltonian systems

TL;DR

This paper introduces a novel structure-preserving model order reduction method for nonlinear port-Hamiltonian systems using generalized manifold Galerkin reduction, maintaining system properties and improving accuracy.

Contribution

It presents the first intrusive structure-preserving MOR approach for nonlinear pH systems based on general nonlinear approximation maps.

Findings

Lower relative reduction error compared to existing methods

Applicable to both linear and nonlinear pH systems

Maintains stability and passivity in reduced models

Abstract

This paper considers structure-preserving model order reduction (MOR) techniques for port-Hamiltonian (pH) systems, which are typically derived from energy-based modelling. To keep favorable properties of pH systems such as stability and passivity in a reduced order model (ROM), we use structure-preserving methods in the reduction process. There exists an extensive literature on structure-preserving MOR methods of pH systems, however, to the best of our knowledge, there does not exist an intrusive structure-preserving MOR method for nonlinear pH systems on the base of general nonlinear approximation maps. To close this gap, we propose a MOR method for pH systems based on the idea of the generalized manifold Galerkin (GMG) reduction. The resulting MOR method can be applied to both linear and nonlinear pH systems resulting in ROMs, which are again of pH form. For the numerical examples, we employ a linear and a nonlinear mass-spring-damper system and the results show that the proposed MOR methods have lower relative reduction error compared to existing methods.