Overcoming the dissipation obstacle with bicomplex port-hamiltonian mechanics

Coen Hutters; Max Mendel

doi:10.1016/j.ifacol.2020.12.1569

Overcoming the dissipation obstacle with bicomplex port-hamiltonian mechanics

Coen Hutters^*, Max Mendel

^*Corresponding author for this work

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

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Abstract

The dissipation obstacle refers to the problem that there is no general solution to shape the energy of dissipative port-Hamiltonian (pH) systems with the method of Casimir functions. This paper argues that it is caused by lack of a strictly symplectic structure of a dissipative port-Hamiltonian system. We develop a method of bicomplex pH systems that is strictly symplectic and we show how it overcomes the obstacle and allows one to systematically use Casimir functions to shape the energy.

Original language	English
Pages (from-to)	5573-5578
Journal	IFAC-PapersOnline
Volume	53 (2020)
Issue number	2
DOIs	https://doi.org/10.1016/j.ifacol.2020.12.1569
Publication status	Published - 2021
Event	21st IFAC World Congress 2020 - Berlin, Germany Duration: 12 Jul 2020 → 17 Jul 2020

Keywords

Dissipation obstacle
Energy shaping
Energy-Casimir method
Hamiltonian mechanics
Port-Hamiltonian systems

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10.1016/j.ifacol.2020.12.1569

1-s2.0-S2405896320321650-mainFinal published version, 447 KBLicence: CC BY-NC-ND

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AB - The dissipation obstacle refers to the problem that there is no general solution to shape the energy of dissipative port-Hamiltonian (pH) systems with the method of Casimir functions. This paper argues that it is caused by lack of a strictly symplectic structure of a dissipative port-Hamiltonian system. We develop a method of bicomplex pH systems that is strictly symplectic and we show how it overcomes the obstacle and allows one to systematically use Casimir functions to shape the energy.

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KW - Energy shaping

KW - Energy-Casimir method

KW - Hamiltonian mechanics

KW - Port-Hamiltonian systems

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Overcoming the dissipation obstacle with bicomplex port-hamiltonian mechanics

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Keywords

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