18 research outputs found
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
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
Port-Hamiltonian systems result from port-based network modeling of physical
systems and are an important example of passive state-space systems. In this
paper, we develop the framework for model reduction of large-scale
multi-input/multi-output port-Hamiltonian systems via tangential rational
interpolation. The resulting reduced-order model not only is a rational
tangential interpolant but also retains the port-Hamiltonian structure; hence
is passive. This reduction methodology is described in both energy and
co-energy system coordinates. We also introduce an -inspired
algorithm for effectively choosing the interpolation points and tangential
directions. The algorithm leads a reduced port-Hamiltonian model that satisfies
a subset of -optimality conditions. We present several numerical
examples that illustrate the effectiveness of the proposed method showing that
it outperforms other existing techniques in both quality and numerical
efficiency