Authors

Ricardo Lopezlena, Jacquelien M.A. Scherpen, Kenji Fujimoto

Abstract

Supported by the framework of dissipativity theory, a procedure based on physical energy to balance and reduce port-Hamiltonian systems with collocated inputs and outputs is presented. Additionally, some relations with the methods of nonlinear balanced reduction are exposed. Finally a structure-preserving reduction method based on singular perturbations is shown

Keywords

Nonlinear systems; model approximation; model reduction

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2003
  • Volume: 36
  • Issue: 2
  • Pages: 69–74
  • Publisher: Elsevier BV
  • DOI: 10.1016/s1474-6670(17)38869-9
  • Note: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control 2003, Seville, Spain, 3-5 April 2003

BibTeX

@article{Lopezlena_2003,
  title={{Energy-Storage Balanced Reduction of Port-Hamiltonian Systems}},
  volume={36},
  ISSN={1474-6670},
  DOI={10.1016/s1474-6670(17)38869-9},
  number={2},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Lopezlena, Ricardo and Scherpen, Jacquelien M.A. and Fujimoto, Kenji},
  year={2003},
  pages={69--74}
}

Download the bib file

References

  • Fujimoto, K. & Scherpen, J. M. A. Model reduction for nonlinear systems based on the differential eigenstructure of Hankel operators. Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) 3252–3257 doi:10.1109/cdc.2001.980322 – 10.1109/cdc.2001.980322
  • Gray, W. S. & Mesko, J. P. Observability functions for linear and nonlinear systems. Systems & Control Letters 38, 99–113 (1999) – 10.1016/s0167-6911(99)00051-1
  • Kato, (1966)
  • Lopezlena, Energy Functions and balancing for discrete -time nonlinear systems. (2002)
  • Marsden, Reduction of Symplectic Manifolds with symmetry. Rep. Math. Phis (1974)
  • Nijmeijer, (1990)
  • van der Schaft, (2000)
  • van der Schaft, System theoretic description of physical systems. CWI Tract 3 (1984)
  • van der Schaft, Slow dynamics of Hamil-tonian systems, unpublished manuscript (2002)
  • van der Schaft, A. Controllability and observability for affine nonlinear Hamiltonian systems. IEEE Trans. Automat. Contr. 27, 490–492 (1982) – 10.1109/tac.1982.1102900
  • van der Schaft, A. J. & Oeloff, J. E. Model reduction of linear conservative mechanical systems. IEEE Trans. Automat. Contr. 35, 729–733 (1990) – 10.1109/9.53555
  • Scherpen, Balancing for Nonlinear Systems. (1994)
  • Scherpen, J. M. A. Balancing for nonlinear systems. Systems & Control Letters 21, 143–153 (1993) – 10.1016/0167-6911(93)90117-o
  • SCHERPEN, J. M. A. & VAN DER SCHAFT, A. J. Normalized coprime factorizations and balancing for unstable nonlinear systems. International Journal of Control 60, 1193–1222 (1994) – 10.1080/00207179408921517
  • – 10.1002/(sici)1099-1239(199608)6:7<645::aid-rnc179>3.0.co;2-x
  • Weiland, Balancing for Model Approximation of Dissipative Dynamical Systems. (1994)
  • Willeins, Dissipative Dynamical Systems. Part I: General Theory. Arch Rational Mech. Anal (1972)