Homogeneous Hamiltonian Control Systems Part I: Geometric Formulation

Authors

Arjan van der Schaft, Bernhard Maschke

Abstract

Contact geometry has been successfully employed for the geometric formulation and control of systems containing thermodynamic components. In this paper we elaborate on the geometric theory of symplectization of contact manifolds in order to lift contact control systems to Hamiltonian control systems with a Hamiltonian that is homogeneous in the co-state variables. This provides a new view on contact control systems as used in thermodynamics, and offers possibilities for unifying the theories of contact control systems, Hamiltonian input-output systems and port-Hamiltonian systems.

Keywords

Hamiltonian systems; nonlinear control; thermodynamics; contact geometry; homogeneous functions; invariant Lagrangian manifolds; liftings

Citation

• Journal: IFAC-PapersOnLine
• Year: 2018
• Volume: 51
• Issue: 3
• Pages: 1–6
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2018.06.001
• Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018

BibTeX

@article{van_der_Schaft_2018,
  title={{Homogeneous Hamiltonian Control Systems Part I: Geometric Formulation}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.06.001},
  number={3},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={van der Schaft, Arjan and Maschke, Bernhard},
  year={2018},
  pages={1--6}
}

Download the bib file

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