Generalized port-Hamiltonian DAE systems
Authors
Arjan van der Schaft, Bernhard Maschke
Abstract
Motivated by recent work in this area we expand on a generalization of port-Hamiltonian systems that is obtained by replacing the Hamiltonian function representing energy storage by a Lagrangian subspace. This leads to a new class of algebraic constraints and DAE systems in physical systems modeling. It is shown how Dirac structures and Lagrangian subspaces allow for similar representations, and how this can be exploited to convert algebraic constraints originating from Dirac structures into algebraic constraints corresponding to Lagrangian subspaces, and conversely.
Keywords
Port-Hamiltonian system; Algebraic constraint; Dirac structure; Lagrangian subspace; DAE system
Citation
- Journal: Systems & Control Letters
- Year: 2018
- Volume: 121
- Issue:
- Pages: 31–37
- Publisher: Elsevier BV
- DOI: 10.1016/j.sysconle.2018.09.008
BibTeX
@article{van_der_Schaft_2018,
title={{Generalized port-Hamiltonian DAE systems}},
volume={121},
ISSN={0167-6911},
DOI={10.1016/j.sysconle.2018.09.008},
journal={Systems & Control Letters},
publisher={Elsevier BV},
author={van der Schaft, Arjan and Maschke, Bernhard},
year={2018},
pages={31--37}
}
References
- Golo, Hamiltonian formulation of bond graphs. (2003)
- van der Schaft, Port-Hamiltonian differential–algebraic systems. (2013)
- van der Schaft, (2017)
- Dalsmo, M. & van der Schaft, A. On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems. SIAM Journal on Control and Optimization vol. 37 54–91 (1998) – 10.1137/s0363012996312039
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
- Mehl, C., Mehrmann, V. & Sharma, P. Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations. SIAM Journal on Matrix Analysis and Applications vol. 37 1625–1654 (2016) – 10.1137/16m1067330
- van der Schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Arch. Elektron. Übertrag.tech. (1995)
- Courant, T. J. Dirac manifolds. Transactions of the American Mathematical Society vol. 319 631–661 (1990) – 10.1090/s0002-9947-1990-0998124-1
- van der Schaft, A. J. & Maschke, B. M. Port-Hamiltonian Systems on Graphs. SIAM Journal on Control and Optimization vol. 51 906–937 (2013) – 10.1137/110840091
- Bloch, Representation of Dirac structures on vector spaces and nonlinear lcv-circuits. (1999)