New insights in the geometry and interconnection of port-Hamiltonian systems
Authors
M Barbero-Liñán, H Cendra, E García-Toraño Andrés, D Martín de Diego
Abstract
We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given throughout the paper to show the applicability and the novel contributions of the proposed framework.
Citation
- Journal: Journal of Physics A: Mathematical and Theoretical
- Year: 2018
- Volume: 51
- Issue: 37
- Pages: 375201
- Publisher: IOP Publishing
- DOI: 10.1088/1751-8121/aad4ba
BibTeX
@article{Barbero_Li_n_2018,
title={{New insights in the geometry and interconnection of port-Hamiltonian systems}},
volume={51},
ISSN={1751-8121},
DOI={10.1088/1751-8121/aad4ba},
number={37},
journal={Journal of Physics A: Mathematical and Theoretical},
publisher={IOP Publishing},
author={Barbero-Liñán, M and Cendra, H and García-Toraño Andrés, E and Martín de Diego, D},
year={2018},
pages={375201}
}
References
- Abraham R, Foundations of Mechanics (1978)
- Barbero-Liñán M, (2018)
- Batlle, C., Massana, I. & Simo, E. Representation of a general composition of Dirac structures. IEEE Conference on Decision and Control and European Control Conference 5199–5204 (2011) doi:10.1109/cdc.2011.6160588 – 10.1109/cdc.2011.6160588
- Blankenstein, G. & van der Schaft, A. J. Symmetry and reduction in implicit generalized Hamiltonian systems. Reports on Mathematical Physics vol. 47 57–100 (2001) – 10.1016/s0034-4877(01)90006-0
- Bursztyn, H. A brief introduction to Dirac manifolds. Geometric and Topological Methods for Quantum Field Theory 4–38 (2013) doi:10.1017/cbo9781139208642.002 – 10.1017/cbo9781139208642.002
- Bursztyn, H. & Radko, O. Gauge equivalence of Dirac structures and symplectic groupoids. Annales de l’institut Fourier vol. 53 309–337 (2003) – 10.5802/aif.1945
- Cendra, H. et al. An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems. Journal of Geometric Mechanics vol. 6 167–236 (2014) – 10.3934/jgm.2014.6.167
- Cendra H, (2017)
- Cervera, J., Schaft, A. J. & Baños, A. On composition of Dirac structures and its implications for control by interconnection. Lecture Notes in Control and Information Sciences 55–63 doi:10.1007/3-540-45802-6_5 – 10.1007/3-540-45802-6_5
- 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
- Courant, T. J. Dirac manifolds. Transactions of the American Mathematical Society vol. 319 631–661 (1990) – 10.1090/s0002-9947-1990-0998124-1
- Courant T, Action Hamiltoniennes de Groupes. Troisième théorème de Lie (Lyon, 1986) (1988)
- 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
- Dorfman I, Nonlinear Science: Theory and Applications (1993)
- Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica vol. 40 757–771 (2004) – 10.1016/j.automatica.2003.12.017
- Gualtieri, M. Generalized complex geometry. Annals of Mathematics vol. 174 75–123 (2011) – 10.4007/annals.2011.174.1.3
- Hairer E, Geometric Numerical Integration (2010)
- O. Jacobs, H. & Yoshimura, H. Tensor products of Dirac structures and interconnection in Lagrangian mechanics. Journal of Geometric Mechanics vol. 6 67–98 (2014) – 10.3934/jgm.2014.6.67
- Liberzon, D. Switching in Systems and Control. Systems & Control: Foundations & Applications (Birkhäuser Boston, 2003). doi:10.1007/978-1-4612-0017-8 – 10.1007/978-1-4612-0017-8
- Marle, C.-M. On symmetries and constants of motion in Hamiltonian systems with nonholonomic constraints. Banach Center Publications (2003) doi:10.4064/bc59-0-12 – 10.4064/bc59-0-12
- Marsden, J. E. & West, M. Discrete mechanics and variational integrators. Acta Numerica vol. 10 357–514 (2001) – 10.1017/s096249290100006x
- Merker, J. On the Geometric Structure of Hamiltonian Systems with Ports. Journal of Nonlinear Science vol. 19 717–738 (2009) – 10.1007/s00332-009-9052-3
- Parks, H. & Leok, M. Variational Integrators for Interconnected Lagrange–Dirac Systems. Journal of Nonlinear Science vol. 27 1399–1434 (2017) – 10.1007/s00332-017-9364-7
- Ramírez, H., Le Gorrec, Y., Maschke, B. & Couenne, F. On the passivity based control of irreversible processes: A port-Hamiltonian approach. Automatica vol. 64 105–111 (2016) – 10.1016/j.automatica.2015.07.002
- 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
- van der Schaft A, AEU. Archiv. Elektron. Übertragungstechnik (1995)
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
- van der Schaft, A. & Schumacher, H. An Introduction to Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences (Springer London, 2000). doi:10.1007/bfb0109998 – 10.1007/bfb0109998
- Yoshimura, H. & Marsden, J. E. Dirac structures in Lagrangian mechanics Part I: Implicit Lagrangian systems. Journal of Geometry and Physics vol. 57 133–156 (2006) – 10.1016/j.geomphys.2006.02.009