Model reduction of port-Hamiltonian systems based on reduction of Dirac structures

The geometric formulation of general port-Hamiltonian systems is used in order to obtain two structure preserving reduction methods. The main idea is to construct a reduced-order Dirac structure corresponding to zero power flow in some of the energy-storage ports. This can be performed in two canonical ways, called the effort- and the flow-constraint methods. We show how the effort-constraint method can be regarded as a projection-based model reduction method

Structure Preserving Moment Matching for Port-Hamiltonian Systems:Arnoldi and Lanczos

Structure preserving model reduction of single-input single-output port-Hamiltonian systems is considered by employing the rational Krylov methods. The rational Arnoldi method is shown to preserve (for the reduced order model) not only a specific number of the moments at an arbitrary point in the complex plane but also the port-Hamiltonian structure. Furthermore, it is shown how the rational Lanczos method applied to a subclass of port-Hamiltonian systems, characterized by an algebraic condition, preserves the port-Hamiltonian structure. In fact, for the same subclass of port-Hamiltonian systems the rational Arnoldi method and the rational Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function