A Tutorial Introduction to Model Reduction for Port-Hamiltonian Systems

The framework of port-Hamiltonian systems is a modeling paradigm and aims for a structured modeling approach that, on the one hand, is close to physics and, on the other hand, is particularly useful when it comes to mathematical analysis, approximation, simulation, and control. One of the major benefits of the model class is that it is closed under interconnection, i.e., we can use a bottom-up modeling approach, where we model each component of a complex dynamical system separately and then interconnect the components via well-defined interconnection ports. After a short introduction to port-Hamiltonian systems, the main focus of this talk is on the construction of low-dimensional representations of port-Hamiltonian systems via structure-preserving model order reduction. We discuss several paths that one can follow and the advantages/disadvantages that come with the respective approach. The theoretical findings are illustrated with several numerical examples.