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. The goal of this paper is to apply a previously developed discrete modeling technique to study the interconnection of continuous systems with discrete ones in such a way that passivity is preserved. Such a theory has potential applications, in the field of haptics, telemanipulation etc. It is shown that our discrete modeling theory can be used to formalize previously developed techniques for obtaining passive interconnections of continuous and discrete systems.

Citation

  • Journal: Proceedings of the 44th IEEE Conference on Decision and Control
  • Year: 2006
  • Volume:
  • Issue:
  • Pages: 5656–5661
  • Publisher: IEEE
  • DOI: 10.1109/cdc.2005.1583064

BibTeX

@inproceedings{Talasila,
  title={{Discrete port-Hamiltonian systems: mixed interconnections}},
  DOI={10.1109/cdc.2005.1583064},
  booktitle={{Proceedings of the 44th IEEE Conference on Decision and Control}},
  publisher={IEEE},
  author={Talasila, V. and Clemente-Gallardo, J. and van der Schaft, A.J.},
  pages={5656--5661}
}

Download the bib file

References

  • van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
  • 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 329, 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
  • talasila, Port hamiltonian systems - a discrete approach. Submitted to Systems and Control Letters (0)
  • van der schaft, The hamiltonian formulation of energy conserving physical systems with external ports. Archiv fur Electronik und Ubertragungstechnik (1995)
  • Talasila, V., Clemente-Gallardo, J. & Schaft, A. J. van der. Geometry and Hamiltonian mechanics on discrete spaces. J. Phys. A: Math. Gen. 37, 9705–9734 (2004) – 10.1088/0305-4470/37/41/008
  • talasila, A hamiltonian approach to discrete mechanics: Issues in geometry, modeling, simulation and control. (2004)
  • Marsden, J. E. & West, M. Discrete mechanics and variational integrators. Acta Numerica 10, 357–514 (2001) – 10.1017/s096249290100006x
  • Putting energy back in control. IEEE Control Syst. 21, 18–33 (2001) – 10.1109/37.915398
  • talasila, Discrete port hamiltonian systems. I FA C Proceedings (2005)
  • talasila, Hamiltonian mechanics on discrete manifolds. Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems Katholieke Universiteit Leuven Belgium (2004)
  • Stramigioli, S., Secchi, C., van der Schaft, A. J. & Fantuzzi, C. Sampled data systems passivity and discrete port-Hamiltonian systems. IEEE Trans. Robot. 21, 574–587 (2005) – 10.1109/tro.2004.842330
  • Stramigioli, S., Secchi, C., van der Schaft, A. J. & Fantuzzi, C. A novel theory for sampled data system passivity. IEEE/RSJ International Conference on Intelligent Robots and System vol. 2 1936–1941 – 10.1109/irds.2002.1044039