Discretized Hamiltonian Systems with Distributed Energy Flows on Divisible Meshes

Authors

Gou Nishida, Bernhard Maschke, Ryojun Ikeura

Abstract

This paper discusses two extensions of the discretization of distributed port-Hamiltonian systems. One of them is the incorporating non-boundary integrable energy flows, called distributed energy structures. The other is the derivation of transformations of basis forms used for dividing and assembling of meshes.

Keywords

algebraic/geometric methods, discretization, hamiltonian systems

Citation

• Journal: IFAC Proceedings Volumes
• Year: 2011
• Volume: 44
• Issue: 1
• Pages: 13474–13479
• Publisher: Elsevier BV
• DOI: 10.3182/20110828-6-it-1002.03219
• Note: 18th IFAC World Congress

BibTeX

@article{Nishida_2011,
  title={{Discretized Hamiltonian Systems with Distributed Energy Flows on Divisible Meshes}},
  volume={44},
  ISSN={1474-6670},
  DOI={10.3182/20110828-6-it-1002.03219},
  number={1},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Nishida, Gou and Maschke, Bernhard and Ikeura, Ryojun},
  year={2011},
  pages={13474--13479}
}

Download the bib file

References

• Thijssen, (1999)
• van der Schaft, (2000)
• Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica 40, 757–771 (2004) – 10.1016/j.automatica.2003.12.017
• Macchelli, Passivity-based control of spatially discretized port-Hamiltonian system. Proc. 8th IFAC Symposium on Nonlinear Control Systems, Bologna (2010)
• Gillette, Notes on Discrete Exterior Calculus (2009)
• Bossavit, Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism. Proc. of the IEEE (1988)
• Desbrun, M., Kanso, E. & Tong, Y. Discrete Differential Forms for Computational Modeling. Oberwolfach Seminars 287–324 doi:10.1007/978-3-7643-8621-4_16 – 10.1007/978-3-7643-8621-4_16
• Stern, A., Tong, Y., Desbrun, M. & Marsden, J. E. Variational Integrators for Maxwell’s Equations with Sources. PIERS Online 4, 711–715 (2008) – 10.2529/piers071019000855
• Morita, (2001)
• van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics 42, 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
• Courant, T. J. Dirac manifolds. Trans. Amer. Math. Soc. 319, 631–661 (1990) – 10.1090/s0002-9947-1990-0998124-1
• Nishida, Topological Geometry and Control for Distributed Port-Hamiltonian Systems with Non-integrable Structures. (2008)