Limit cycles in locally Hamiltonian systems with dissipation

Fernando Castaños; Dmitry Gromov

doi:10.1016/j.ifacol.2021.11.077

Limit cycles in locally Hamiltonian systems with dissipation

Fernando Castaños^*
, Dmitry Gromov

^*Corresponding author for this work

Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
St. Petersburg State University

Research output: Contribution to journal › Conference article › peer-review

Abstract

We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power of port-Hamiltonian systems by providing a framework to model cyclic physical processes for energy conversion and extraction.

Original language	English
Pages (from-to)	192-197
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	54
Issue number	19
DOIs	https://doi.org/10.1016/j.ifacol.2021.11.077
Publication status	Published - 2021
Externally published	Yes
Event	7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021 - Berlin, Germany Duration: 11 Oct 2021 → 13 Oct 2021

Keywords

Discontinuous Hamiltonian
Limit cycles
Locally Hamiltonian systems
Passivity
Port-Hamiltonian systems
Symplectic systems

Access to Document

10.1016/j.ifacol.2021.11.077

Cite this

@article{5b8e6bd51589417a93912d2748f94b18,

title = "Limit cycles in locally Hamiltonian systems with dissipation",

abstract = "We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power of port-Hamiltonian systems by providing a framework to model cyclic physical processes for energy conversion and extraction.",

keywords = "Discontinuous Hamiltonian, Limit cycles, Locally Hamiltonian systems, Passivity, Port-Hamiltonian systems, Symplectic systems",

author = "Fernando Casta{\~n}os and Dmitry Gromov",

note = "Publisher Copyright: {\textcopyright} The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021 ; Conference date: 11-10-2021 Through 13-10-2021",

year = "2021",

doi = "10.1016/j.ifacol.2021.11.077",

language = "English",

volume = "54",

pages = "192--197",

journal = "IFAC-PapersOnLine",

issn = "2405-8971",

publisher = "Elsevier B.V.",

number = "19",

}

TY - JOUR

T1 - Limit cycles in locally Hamiltonian systems with dissipation

AU - Castaños, Fernando

AU - Gromov, Dmitry

N1 - Publisher Copyright: © The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

PY - 2021

Y1 - 2021

N2 - We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power of port-Hamiltonian systems by providing a framework to model cyclic physical processes for energy conversion and extraction.

AB - We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power of port-Hamiltonian systems by providing a framework to model cyclic physical processes for energy conversion and extraction.

KW - Discontinuous Hamiltonian

KW - Limit cycles

KW - Locally Hamiltonian systems

KW - Passivity

KW - Port-Hamiltonian systems

KW - Symplectic systems

UR - https://www.scopus.com/pages/publications/85121007003

U2 - 10.1016/j.ifacol.2021.11.077

DO - 10.1016/j.ifacol.2021.11.077

M3 - Conference article

AN - SCOPUS:85121007003

SN - 2405-8971

VL - 54

SP - 192

EP - 197

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 19

T2 - 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021

Y2 - 11 October 2021 through 13 October 2021

ER -

Limit cycles in locally Hamiltonian systems with dissipation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this