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Control of port-Hamiltonian differential-algebraic systems and applications

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  11 May 2023

Volker Mehrmann Open the ORCID record for Volker Mehrmann [Opens in a new window]  and
Benjamin Unger
Volker Mehrmann
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany E-mail: mehrmann@math.tu-berlin.de
Benjamin Unger
Affiliation:
Stuttgart Center for Simulation Science, University of Stuttgart, Universitätsstrasse 32, 70569 Stuttgart, Germany E-mail: benjamin.unger@simtech.uni-stuttgart.de
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Abstract

We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control. The structure is ideal for automated network-based modelling since it is invariant under power-conserving interconnection, congruence transformations and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity and numerical methods to check these properties.

After recalling the concepts for general linear and nonlinear descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analysed, and time discretization and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed.

The properties of port-Hamiltonian descriptor systems and their use in modelling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

MSC classification

Primary: 65L80: Methods for differential-algebraic equations
Type
Research Article
Information
Acta Numerica , Volume 32 , May 2023 , pp. 395 - 515
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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