Contraction Theory and Differential Passivity in the port-Hamiltonian formalism

Authors

Mario Spirito, Bernhard Maschke, Yann Le Gorrec

Abstract

In this work, we recall the concept of contractive dynamics and its natural extension to the notion of Differential dissipativity/passivity via the use of the so-called prolonged (or extended) system dynamics, obtained by lifting the system to the tangent bundle of the underlying manifold. The new concept of dissipative Differential Hamiltonian dynamics is proposed providing a weaker notion of contractive dynamical system. Furthermore, the Differential Hamiltonian notion is extended to the definition of Differentially passive port-Hamiltonian system. We describe explicit conditions to exploit the ‘natural’ Differential Hamiltonian function as differential storage function for the port-Hamiltonian system dynamics.

Keywords

Contractive systems; Differential passivity; port-Hamiltonian systems; dissipative Hamiltonian systems; dissipative Differential Hamiltonian system

Citation

• Journal: IFAC-PapersOnLine
• Year: 2024
• Volume: 58
• Issue: 6
• Pages: 184–189
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2024.08.278
• Note: 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024- Besançon, France, June 10 – 12, 2024

BibTeX

@article{Spirito_2024,
  title={{Contraction Theory and Differential Passivity in the port-Hamiltonian formalism}},
  volume={58},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2024.08.278},
  number={6},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Spirito, Mario and Maschke, Bernhard and Le Gorrec, Yann},
  year={2024},
  pages={184--189}
}

Download the bib file

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