Structure-Preserving Generalized Manifold Galerkin Reduction for Port-Hamiltonian Systems

This paper considers structure-preserving model order reduction (MOR) techniques for port-Hamiltonian (pH) systems, which are typically derived from energy-based modeling. To keep favorable properties of \pH systems such as passivity in a reduced order model (ROM), we use structure-preserving methods in the reduction process. Although projection-based structure-preserving MOR methods for nonlinear pH systems based on nonlinear approximation ansatzes have recently been proposed, existing approaches typically rely on specific structures of the approximation map and the underlying pH system. To address this limitation, we propose a \MOR framework based on generalized manifold Galerkin (GMG) reduction. The resulting framework can employ general nonlinear approximation maps while preserving the pH structure. We establish sufficient conditions for structure preservation, show that the associated non-degeneracy conditions are generically satisfied. We further present linear and quadratic approximation maps within the proposed framework. Numerical examples for a linear and a nonlinear mass-spring-damper system show that the proposed \MOR methods have lower relative reduction error compared to existing methods.