TY - JOUR A1 - Breiten, Tobias A1 - Morandin, Riccardo A1 - Schulze, Philipp T1 - Error bounds for port-Hamiltonian model and controller reduction based on system balancing N2 - Linear quadratic Gaussian (LQG) control design for port-Hamiltonian systems is studied. The recently proposed method from [42] is reviewed and modified such that the resulting controllers have a port-Hamiltonian (pH) realization. Based on this new modification, a reduced-order controller is obtained by truncation of a balanced system. The approach is shown to be closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. With regard to this error bound, a theoretically optimal pH-representation is derived. Consequences for pH-preserving balanced truncation model reduction are discussed and shown to yield two different classical H∞ -error bounds. Numerical examples illustrate the main theoretical findings. KW - port-Hamiltonian systems KW - model order reduction KW - LQG control design KW - error bound Y1 - 2020 U6 - https://doi.org/10.1016/j.camwa.2021.07.022 CY - Computers & Mathematics with Applications ER - TY - INPR A1 - Mehrmann, Volker A1 - Morandin, Riccardo T1 - Structure-preserving discretization for port-Hamiltonian descriptor systems N2 - We extend the modeling framework of port-Hamiltonian descriptor systems to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its energy balance properties. In particular, port-Hamiltonian systems are naturally passive and Lyapunov stable, because the Hamiltonian defines a Lyapunov function. The explicit representation of input and dissipation in the structure make these systems particularly suitable for output feedback control. It is shown that this structure is invariant under a wide class of nonlinear transformations, and that it can be naturally modularized, making it adequate for automated modeling. We investigate then the application of time-discretization schemes to these systems and we show that, under certain assumptions on the Hamiltonian, structure preservation is achieved for some methods. Numerical examples are provided. KW - port-Hamiltonian systems KW - structure-preserving discretization KW - differential-algebraic equations KW - Dirac structure Y1 - 2021 ER - TY - INPR A1 - Domschke, Pia A1 - Hiller, Benjamin A1 - Lang, Jens A1 - Mehrmann, Volker A1 - Morandin, Riccardo A1 - Tischendorf, Caren T1 - Gas Network Modeling: An Overview N2 - With this overview we want to provide a compilation of different models for the description of gas flow in networks in order to facilitate the introduction to the topic. Special attention is paid to the hierarchical structure inherent to the modeling, and the detailed description of individual components such as valves and compressors. Also included are network model classes based on purely algebraic relations, and energy-based port-Hamiltonian models. A short overview of basic numerical methods and concepts for the treatment of hyperbolic balance equations is also given. We do not claim completeness and refer in many places to the existing literature. The idea of a model catalog came to us in the context of the application for the CRC/Transregio 154 ``Mathematical modeling, simulation and optimization using the example of gas networks''. The present English translation is an extension from [P. Domschke, B. Hiller, J. Lang, and C. Tischendorf. Modellierung von Gasnetzwerken: Eine Übersicht. Preprint, TRR 154, 2017]. At this point we would like to thank the DFG for its support. Y1 - 2021 ER - TY - INPR A1 - Domschke, Pia A1 - Giesselmann, Jan A1 - Lang, Jens A1 - Breiten, Tobias A1 - Mehrmann, Volker A1 - Morandin, Riccardo A1 - Hiller, Benjamin A1 - Tischendorf, Caren T1 - Gas Network Modeling: An Overview (Extended English Version) N2 - With this overview we want to provide a compilation of different models for the description of gas flow in networks in order to facilitate the introduction to the topic. Special attention is paid to the hierarchical structure inherent to the modeling, and the detailed description of individual components such as valves and compressors. Also included are network model classes based on purely algebraic relations, and energy-based port-Hamiltonian models. A short overview of basic numerical methods and concepts for the treatment of hyperbolic balance equations is also given. We do not claim completeness and refer in many places to the existing literature. Y1 - 2023 ER - TY - INPR A1 - Breiten, Tobias A1 - Karsai, Attila A1 - Mehrmann, Volker A1 - Domschke, Pia A1 - Giesselmann, Jan A1 - Lang, Jens A1 - Tscherpel, Tabea A1 - Hiller, Benjamin A1 - Morandin, Riccardo A1 - Tischendorf, Caren T1 - A Catalog of Gas Network Models: PDEs, Coupling Conditions, and Numerical Schemes N2 - This document aims to provide a concise and clear introduction to the topic of gas flow modeling. We present several models for gas flow, organized into hierarchies based on complexity. We discuss in detail the modeling of individual components such as valves and compressors. Network model classes based on purely algebraic relations and energy-based port-Hamiltonian models are included, along with a brief overview of basic numerical methods for hyperbolic balance laws and port-Hamiltonian systems. We do not claim completeness and refer in many places to the existing literature. Y1 - N1 - This is an updated version of [P. Domschke, B. Hiller, J. Lang, V. Mehrmann, R. Morandin, and C. Tischendorf. Gas Network Modeling: An Overview. Preprint, TRR 154, 2021], available at: https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/411 ER -