Overcoming the dissipation obstacle with bicomplex port-hamiltonian mechanics

Journal article (2021)

Authors

C. Hutters Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
M.B. Mendel Support Delft Center for Systems and Control - Mechanical, Maritime and Materials Engineering
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2021 C. Hutters, M.B. Mendel
DOI: https://doi.org/10.1016/j.ifacol.2020.12.1569
Hamiltonian mechanics Port-Hamiltonian systems Dissipation obstacle Energy shaping Energy-Casimir method
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Published Date

2021

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

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.