Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection

A. Macchelli, Alessandro Macchelli, Arjan van der Schaft, Claudio Melchiorri

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

19 Citations (Scopus)
24 Downloads (Pure)

Abstract

In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by extending the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. Consequently, it seems natural that also finite dimensional control methodologies developed for finite dimensional port Hamiltonian systems can be extended in order to cope with infinite dimensional systems. In this paper, the control by interconnection and energy shaping methodology is applied to the stabilization problem of a distributed parameter system by means of a finite dimensional controller. The key point is the generalization of the definition of Casimir function to the hybrid case, i.e. when the dynamical system to be considered results from the power conserving interconnection of an infinite and a finite dimensional part. A simple application concerning the stabilization of the one-dimensional heat equation is presented.
Original languageUndefined
Title of host publicationProceedings of the 43rd IEEE Conference on Decision and Control
Place of PublicationParadise Island, The Bahamas
PublisherIEEE
Pages3768-3773
Number of pages6
ISBN (Print)0-7803-8682-5
Publication statusPublished - Dec 2004
Event43rd IEEE Conference on Decision and Control, CDC 2004 - The Atlantis, Paradise Island, Bahamas
Duration: 14 Dec 200417 Dec 2004
Conference number: 43

Publication series

Name
PublisherIEEE
Volume4
ISSN (Print)0191-2216

Conference

Conference43rd IEEE Conference on Decision and Control, CDC 2004
Abbreviated titleCDC
CountryBahamas
CityParadise Island
Period14/12/0417/12/04

Keywords

  • IR-69161
  • METIS-220423
  • EWI-16814

Cite this

Macchelli, A., Macchelli, A., van der Schaft, A., & Melchiorri, C. (2004). Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. In Proceedings of the 43rd IEEE Conference on Decision and Control (pp. 3768-3773). Paradise Island, The Bahamas: IEEE.
Macchelli, A. ; Macchelli, Alessandro ; van der Schaft, Arjan ; Melchiorri, Claudio. / Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. Proceedings of the 43rd IEEE Conference on Decision and Control. Paradise Island, The Bahamas : IEEE, 2004. pp. 3768-3773
@inproceedings{c2ddd86076164b1e941c426cf6418c8d,
title = "Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection",
abstract = "In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by extending the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. Consequently, it seems natural that also finite dimensional control methodologies developed for finite dimensional port Hamiltonian systems can be extended in order to cope with infinite dimensional systems. In this paper, the control by interconnection and energy shaping methodology is applied to the stabilization problem of a distributed parameter system by means of a finite dimensional controller. The key point is the generalization of the definition of Casimir function to the hybrid case, i.e. when the dynamical system to be considered results from the power conserving interconnection of an infinite and a finite dimensional part. A simple application concerning the stabilization of the one-dimensional heat equation is presented.",
keywords = "IR-69161, METIS-220423, EWI-16814",
author = "A. Macchelli and Alessandro Macchelli and {van der Schaft}, Arjan and Claudio Melchiorri",
year = "2004",
month = "12",
language = "Undefined",
isbn = "0-7803-8682-5",
publisher = "IEEE",
pages = "3768--3773",
booktitle = "Proceedings of the 43rd IEEE Conference on Decision and Control",
address = "United States",

}

Macchelli, A, Macchelli, A, van der Schaft, A & Melchiorri, C 2004, Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. in Proceedings of the 43rd IEEE Conference on Decision and Control. IEEE, Paradise Island, The Bahamas, pp. 3768-3773, 43rd IEEE Conference on Decision and Control, CDC 2004, Paradise Island, Bahamas, 14/12/04.

Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. / Macchelli, A.; Macchelli, Alessandro; van der Schaft, Arjan; Melchiorri, Claudio.

Proceedings of the 43rd IEEE Conference on Decision and Control. Paradise Island, The Bahamas : IEEE, 2004. p. 3768-3773.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection

AU - Macchelli, A.

AU - Macchelli, Alessandro

AU - van der Schaft, Arjan

AU - Melchiorri, Claudio

PY - 2004/12

Y1 - 2004/12

N2 - In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by extending the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. Consequently, it seems natural that also finite dimensional control methodologies developed for finite dimensional port Hamiltonian systems can be extended in order to cope with infinite dimensional systems. In this paper, the control by interconnection and energy shaping methodology is applied to the stabilization problem of a distributed parameter system by means of a finite dimensional controller. The key point is the generalization of the definition of Casimir function to the hybrid case, i.e. when the dynamical system to be considered results from the power conserving interconnection of an infinite and a finite dimensional part. A simple application concerning the stabilization of the one-dimensional heat equation is presented.

AB - In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by extending the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. Consequently, it seems natural that also finite dimensional control methodologies developed for finite dimensional port Hamiltonian systems can be extended in order to cope with infinite dimensional systems. In this paper, the control by interconnection and energy shaping methodology is applied to the stabilization problem of a distributed parameter system by means of a finite dimensional controller. The key point is the generalization of the definition of Casimir function to the hybrid case, i.e. when the dynamical system to be considered results from the power conserving interconnection of an infinite and a finite dimensional part. A simple application concerning the stabilization of the one-dimensional heat equation is presented.

KW - IR-69161

KW - METIS-220423

KW - EWI-16814

M3 - Conference contribution

SN - 0-7803-8682-5

SP - 3768

EP - 3773

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

PB - IEEE

CY - Paradise Island, The Bahamas

ER -

Macchelli A, Macchelli A, van der Schaft A, Melchiorri C. Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. In Proceedings of the 43rd IEEE Conference on Decision and Control. Paradise Island, The Bahamas: IEEE. 2004. p. 3768-3773