Port Hamiltonian formulation of infinite dimensional systems: I. Modeling

Alessandro Macchelli; Arjan van der Schaft; Claudio Melchiorri

doi:10.1109/CDC.2004.1429324

Port Hamiltonian formulation of infinite dimensional systems: I. Modeling

Alessandro Macchelli, Arjan van der Schaft, Claudio Melchiorri

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

52 Citations (Scopus)

116 Downloads (Pure)

Abstract

In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables.

Original language	English
Title of host publication	Proceedings of the 43rd IEEE Conference on Decision and Control 2004
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	3762-3767
Number of pages	6
ISBN (Print)	0-7803-8682-5
DOIs	https://doi.org/10.1109/CDC.2004.1429324
Publication status	Published - Dec 2004
Event	43rd IEEE Conference on Decision and Control, CDC 2004 - The Atlantis, Paradise Island, Bahamas Duration: 14 Dec 2004 → 17 Dec 2004 Conference number: 43

Publication series

Name	Proceedings IEEE Conference on Decision and Control (CDC)
Publisher	IEEE
Number	43
Volume	2004
ISSN (Print)	0191-2216

Conference

Conference	43rd IEEE Conference on Decision and Control, CDC 2004
Abbreviated title	CDC
Country/Territory	Bahamas
City	Paradise Island
Period	14/12/04 → 17/12/04

Keywords

n/a OA procedure

Access to Document

10.1109/CDC.2004.1429324

Cite this

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title = "Port Hamiltonian formulation of infinite dimensional systems: I. Modeling",

abstract = "In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables.",

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author = "Alessandro Macchelli and {van der Schaft}, Arjan and Claudio Melchiorri",

year = "2004",

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language = "English",

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series = "Proceedings IEEE Conference on Decision and Control (CDC)",

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note = "43rd IEEE Conference on Decision and Control, CDC 2004, CDC ; Conference date: 14-12-2004 Through 17-12-2004",

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Macchelli, A, van der Schaft, A & Melchiorri, C 2004, Port Hamiltonian formulation of infinite dimensional systems: I. Modeling. in Proceedings of the 43rd IEEE Conference on Decision and Control 2004. Proceedings IEEE Conference on Decision and Control (CDC), no. 43, vol. 2004, IEEE, Piscataway, NJ, pp. 3762-3767, 43rd IEEE Conference on Decision and Control, CDC 2004, Paradise Island, Bahamas, 14/12/04. https://doi.org/10.1109/CDC.2004.1429324

Port Hamiltonian formulation of infinite dimensional systems: I. Modeling. / Macchelli, Alessandro; van der Schaft, Arjan; Melchiorri, Claudio.
Proceedings of the 43rd IEEE Conference on Decision and Control 2004. Piscataway, NJ: IEEE, 2004. p. 3762-3767 (Proceedings IEEE Conference on Decision and Control (CDC); Vol. 2004, No. 43).

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

TY - GEN

T1 - Port Hamiltonian formulation of infinite dimensional systems

T2 - 43rd IEEE Conference on Decision and Control, CDC 2004

AU - Macchelli, Alessandro

AU - van der Schaft, Arjan

AU - Melchiorri, Claudio

N1 - Conference code: 43

PY - 2004/12

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N2 - In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables.

AB - In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multivariable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables.

KW - n/a OA procedure

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DO - 10.1109/CDC.2004.1429324

M3 - Conference contribution

SN - 0-7803-8682-5

T3 - Proceedings IEEE Conference on Decision and Control (CDC)

SP - 3762

EP - 3767

BT - Proceedings of the 43rd IEEE Conference on Decision and Control 2004

PB - IEEE

CY - Piscataway, NJ

Y2 - 14 December 2004 through 17 December 2004

ER -

Port Hamiltonian formulation of infinite dimensional systems: I. Modeling

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