Authors

Dina Shona Laila, Alessandro Astolfi

Abstract

The issues of constructing a discrete-time model for Hamiltonian systems are in general different from those for dissipative systems. We propose an algorithm for constructing an approximate discrete-time model, which guarantees Hamiltonian conservation. We show that the algorithm also preserves, in a weaker sense, the losslessness property of a class of port-controlled Hamiltonian systems. An application of the algorithm to port-controlled Hamiltonian systems with quadratic Hamiltonian is presented, and we use this to solve the stabilization problem for this class of systems based on the approximate discrete-time model constructed using the proposed algorithm. We illustrate the usefulness of the algorithm in designing a discrete-time controller to stabilize the angular velocity of the dynamics of a rigid body.

Keywords

Hamiltonian systems; Discrete-time systems; Hamiltonian conservation; Stabilization; Nonlinear systems

Citation

  • Journal: Systems & Control Letters
  • Year: 2006
  • Volume: 55
  • Issue: 8
  • Pages: 673–680
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.sysconle.2005.09.012
  • Note: New Trends in Nonlinear Control

BibTeX

@article{Laila_2006,
  title={{Construction of discrete-time models for port-controlled Hamiltonian systems with applications}},
  volume={55},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2005.09.012},
  number={8},
  journal={Systems & Control Letters},
  publisher={Elsevier BV},
  author={Laila, Dina Shona and Astolfi, Alessandro},
  year={2006},
  pages={673--680}
}

Download the bib file

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