Fluid dynamical systems as Hamiltonian boundary control systems

A.J. van der Schaft; B.M. Maschke

doi:10.1109/.2001.980911

Fluid dynamical systems as Hamiltonian boundary control systems

A.J. van der Schaft, B.M. Maschke

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems as recently provided in [11, 12] can be adapted to formulate ideal isentropic compressible fluids with non-zero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure introduced in [11] to a Dirac structure defined on the space of mass density 3-forms and velocity 1-forms, incorporating three-dimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.

Original language	English
Title of host publication	Proceedings of the 40th IEEE Conference on Decision and Control, CDC 2001
Place of Publication	Los Alamitos, CA
Publisher	IEEE
Pages	4497-4502
Number of pages	6
ISBN (Print)	0-7803-7061-9
DOIs	https://doi.org/10.1109/.2001.980911
Publication status	Published - 2001
Event	40th IEEE Conference on Decision and Control, CDC 2001 - Hyatt Regency Grand Cypress, Orlando, United States Duration: 4 Dec 2001 → 7 Dec 2001

Conference

Conference	40th IEEE Conference on Decision and Control, CDC 2001
Abbreviated title	CDC
Country/Territory	United States
City	Orlando
Period	4/12/01 → 7/12/01

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VanderSchaft2001fluidFinal published version, 306 KB

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Fluid dynamical systems as Hamiltonian boundary control systems
van der Schaft, A. J. & Maschke, B. M., 2001, Enschede: University of Twente. (Memorandum / Faculty of Mathematical Sciences; no. 1575)
Research output: Book/Report › Report › Other research output

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AU - Maschke, B.M.

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AB - It is shown how the geometric framework for distributed-parameter port-controlled Hamiltonian systems as recently provided in [11, 12] can be adapted to formulate ideal isentropic compressible fluids with non-zero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac structure introduced in [11] to a Dirac structure defined on the space of mass density 3-forms and velocity 1-forms, incorporating three-dimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.

U2 - 10.1109/.2001.980911

DO - 10.1109/.2001.980911

M3 - Conference contribution

SN - 0-7803-7061-9

SP - 4497

EP - 4502

BT - Proceedings of the 40th IEEE Conference on Decision and Control, CDC 2001

PB - IEEE

CY - Los Alamitos, CA

T2 - 40th IEEE Conference on Decision and Control, CDC 2001

Y2 - 4 December 2001 through 7 December 2001

ER -

Fluid dynamical systems as Hamiltonian boundary control systems

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Fluid dynamical systems as Hamiltonian boundary control systems

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