Discrete port-Hamiltonian systems

Authors

V. Talasila, J. Clemente-Gallardo, A.J. van der Schaft

Abstract

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. One of the goals of this paper is to model port-Hamiltonian systems at the discrete level. We also show that the dynamics of the discrete models we obtain exactly correspond to the dynamics obtained via a usual discretization procedure. In this sense we offer an alternative to the usual procedure of modeling (at the smooth level) and discretization.

Keywords

Discrete mechanics; Port Hamiltonian systems

Citation

• Journal: Systems & Control Letters
• Year: 2006
• Volume: 55
• Issue: 6
• Pages: 478–486
• Publisher: Elsevier BV
• DOI: 10.1016/j.sysconle.2005.10.001

BibTeX

@article{Talasila_2006,
  title={{Discrete port-Hamiltonian systems}},
  volume={55},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2005.10.001},
  number={6},
  journal={Systems & Control Letters},
  publisher={Elsevier BV},
  author={Talasila, V. and Clemente-Gallardo, J. and van der Schaft, A.J.},
  year={2006},
  pages={478--486}
}

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References

• 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
• Zhong, G. & Marsden, J. E. Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators. Physics Letters A vol. 133 134–139 (1988) – 10.1016/0375-9601(88)90773-6
• Hiptmair, R. Discrete Hodge-Operators: An Algebraic Perspective. Progress In Electromagnetics Research vol. 32 247–269 (2001) – 10.2528/pier00080110
• Marsden, J. E. & West, M. Discrete mechanics and variational integrators. Acta Numerica vol. 10 357–514 (2001) – 10.1017/s096249290100006x
• Maschke, B. M., Van Der Schaft, A. J. & Breedveld, P. C. An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute vol. 329 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
• Nesic, D. & Teel, A. R. A Framework for Stabilization of Nonlinear Sampled-Data Systems Based on Their Approximate Discrete-Time Models. IEEE Transactions on Automatic Control vol. 49 1103–1122 (2004) – 10.1109/tac.2004.831175
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Sanz-Serna, (1994)
• Talasila, V., Clemente-Gallardo, J. & Schaft, A. J. van der. Geometry and Hamiltonian mechanics on discrete spaces. Journal of Physics A: Mathematical and General vol. 37 9705–9734 (2004) – 10.1088/0305-4470/37/41/008
• Talasila, V., Clemente-Gallardo, J. & van der Schaft, A. J. DISCRETE PORT HAMILTONIAN SYSTEMS. IFAC Proceedings Volumes vol. 38 495–500 (2005) – 10.3182/20050703-6-cz-1902.00737
• van der Schaft, Interconnection and geometry. (1999)
• van der Schaft, (2000)