# Model reduction techniques for linear constant coefficient port-Hamiltonian differential-algebraic systems

## TL;DR

This paper develops and adapts model reduction techniques specifically for large-scale port-Hamiltonian differential-algebraic systems, ensuring structure preservation and constraint integrity, with applications to flow and mechanical systems.

## Contribution

It introduces adapted model reduction methods for port-Hamiltonian differential-algebraic systems, combining Dirac structure reduction and moment matching techniques.

## Key findings

- Methods effectively reduce model size while preserving structure.
- Validated on flow and multibody system benchmarks.
- Maintains algebraic constraints during reduction.

## Abstract

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the state space dimension of such systems may be very large, in particular when the model is a space-discretized partial differential-algebraic system, in optimization and control there is a need for model reduction methods that preserve the port-Hamiltonian structure while keeping the (explicit and implicit) algebraic constraints unchanged. To combine model reduction for differential-algebraic equations with port-Hamiltonian structure preservation, we adapt two classes of techniques (reduction of the Dirac structure and moment matching) to handle port-Hamiltonian differential-algebraic equations. The performance of the methods is investigated for benchmark examples originating from semi-discretized flow problems and mechanical multibody systems.