A geometric framework for discrete time port‐Hamiltonian systems
Authors
Karim Cherifi, Hannes Gernandt, Dorothea Hinsen, Volker Mehrmann
Abstract
Port‐Hamiltonian systems provide an energy‐based formulation with a model class that is closed under structure preserving interconnection. For continuous‐time systems, these interconnections are constructed by geometric objects called Dirac structures. In this paper, we derive this geometric formulation and the interconnection properties for scattering passive discrete‐time port‐Hamiltonian systems.
Citation
- Journal: PAMM
- Year: 2023
- Volume: 23
- Issue: 2
- Pages:
- Publisher: Wiley
- DOI: 10.1002/pamm.202300149
BibTeX
@article{Cherifi_2023,
title={{A geometric framework for discrete time port‐Hamiltonian systems}},
volume={23},
ISSN={1617-7061},
DOI={10.1002/pamm.202300149},
number={2},
journal={PAMM},
publisher={Wiley},
author={Cherifi, Karim and Gernandt, Hannes and Hinsen, Dorothea and Mehrmann, Volker},
year={2023}
}
References
- Gernandt, H., Haller, F. E. & Reis, T. A Linear Relation Approach to Port-Hamiltonian Differential-Algebraic Equations. SIAM Journal on Matrix Analysis and Applications vol. 42 1011–1044 (2021) – 10.1137/20m1371166
- Mehrmann V., Differential‐algebraic systems with dissipative hamiltonian structure. Mathematics of Control, Signals, and Systems (2023)
- Schaft A., Linear port‐hamiltonian dae systems revisited. Systems and Control Letters (2023)
- van der Schaft, A. & Maschke, B. Generalized port-Hamiltonian DAE systems. Systems & Control Letters vol. 121 31–37 (2018) – 10.1016/j.sysconle.2018.09.008
- van der Schaft, A. & Maschke, B. Dirac and Lagrange Algebraic Constraints in Nonlinear Port-Hamiltonian Systems. Vietnam Journal of Mathematics vol. 48 929–939 (2020) – 10.1007/s10013-020-00419-x
- Bankmann, D. & Voigt, M. On linear-quadratic optimal control of implicit difference equations. IMA Journal of Mathematical Control and Information vol. 36 779–833 (2018) – 10.1093/imamci/dny007
- Brüll T., Explicit solutions of regular linear discrete‐time descriptor systems with constant coefficients. The Electronic Journal of Linear Algebra (2009)
- Singular Control Systems. Lecture Notes in Control and Information Sciences (Springer-Verlag, 1989). doi:10.1007/bfb0002475 – 10.1007/bfb0002475
- The Autonomous Linear Quadratic Control Problem. Lecture Notes in Control and Information Sciences (Springer-Verlag, 1991). doi:10.1007/bfb0039443 – 10.1007/bfb0039443
- Cherifi, K., Gernandt, H., Hinsen, D. & Mehrmann, V. On discrete-time dissipative port-Hamiltonian (descriptor) systems. Mathematics of Control, Signals, and Systems vol. 36 561–599 (2023) – 10.1007/s00498-023-00376-z
- Mehrmann, V. & Morandin, R. Structure-preserving discretization for port-Hamiltonian descriptor systems. 2019 IEEE 58th Conference on Decision and Control (CDC) 6863–6868 (2019) doi:10.1109/cdc40024.2019.9030180 – 10.1109/cdc40024.2019.9030180
- Mehrmann, V. & Unger, B. Control of port-Hamiltonian differential-algebraic systems and applications. Acta Numerica vol. 32 395–515 (2023) – 10.1017/s0962492922000083
- van der Schaft, A. & Maschke, B. Generalized port-Hamiltonian DAE systems. Systems & Control Letters vol. 121 31–37 (2018) – 10.1016/j.sysconle.2018.09.008
- Kurula, M. & Staffans, O. A complete model of a finite-dimensional impedance-passive system. Mathematics of Control, Signals, and Systems vol. 19 23–63 (2006) – 10.1007/s00498-006-0008-y
- Mehl, C., Mehrmann, V. & Wojtylak, M. Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems. SIAM Journal on Matrix Analysis and Applications vol. 39 1489–1519 (2018) – 10.1137/18m1164275
- Cervera, J., van der Schaft, A. J. & Baños, A. Interconnection of port-Hamiltonian systems and composition of Dirac structures. Automatica vol. 43 212–225 (2007) – 10.1016/j.automatica.2006.08.014
- Mistiri, F. & Wang, A. P. The Star-product and its Algebraic Properties. Journal of the Franklin Institute vol. 321 21–38 (1986) – 10.1016/0016-0032(86)90053-0
- Redheffer, R. On the Relation of Transmission‐Line Theory to Scattering and Transfer. Journal of Mathematics and Physics vol. 41 1–41 (1962) – 10.1002/sapm19624111