Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

Aditya A. Paranjape; Soon Jo Chung

doi:10.1109/CDC.2015.7402291

Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

Aditya A. Paranjape, Soon Jo Chung

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

1 Citation (Scopus)

Abstract

In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs.

Original language	English
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	578-583
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7402291
Publication status	Published - 2015
Externally published	Yes
Event	IEEE Conference on Decision and Control 2015 - Osaka, Japan Duration: 15 Dec 2015 → 18 Dec 2015 Conference number: 54th https://ieeexplore.ieee.org/xpl/conhome/7396016/proceeding (Proceedings)

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	IEEE Conference on Decision and Control 2015
Abbreviated title	CDC 2015
Country/Territory	Japan
City	Osaka
Period	15/12/15 → 18/12/15
Internet address	https://ieeexplore.ieee.org/xpl/conhome/7396016/proceeding (Proceedings)

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10.1109/CDC.2015.7402291

Cite this

Paranjape, A. A., & Chung, S. J. (2015). Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 578-583). (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2015.7402291

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title = "Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping",

abstract = "In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs.",

author = "Paranjape, {Aditya A.} and Chung, {Soon Jo}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; IEEE Conference on Decision and Control 2015, CDC 2015 ; Conference date: 15-12-2015 Through 18-12-2015",

year = "2015",

doi = "10.1109/CDC.2015.7402291",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

pages = "578--583",

booktitle = "54rd IEEE Conference on Decision and Control,CDC 2015",

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Paranjape, AA & Chung, SJ 2015, Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping. in 54rd IEEE Conference on Decision and Control,CDC 2015. Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, IEEE, Institute of Electrical and Electronics Engineers, pp. 578-583, IEEE Conference on Decision and Control 2015, Osaka, Japan, 15/12/15. https://doi.org/10.1109/CDC.2015.7402291

Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping. / Paranjape, Aditya A.; Chung, Soon Jo.
54rd IEEE Conference on Decision and Control,CDC 2015. IEEE, Institute of Electrical and Electronics Engineers, 2015. p. 578-583 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

TY - GEN

T1 - Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

AU - Paranjape, Aditya A.

AU - Chung, Soon Jo

N1 - Conference code: 54th

PY - 2015

Y1 - 2015

N2 - In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs.

AB - In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs.

UR - http://www.scopus.com/inward/record.url?scp=84962018989&partnerID=8YFLogxK

U2 - 10.1109/CDC.2015.7402291

DO - 10.1109/CDC.2015.7402291

M3 - Conference Paper

AN - SCOPUS:84962018989

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 578

EP - 583

BT - 54rd IEEE Conference on Decision and Control,CDC 2015

PB - IEEE, Institute of Electrical and Electronics Engineers

T2 - IEEE Conference on Decision and Control 2015

Y2 - 15 December 2015 through 18 December 2015

ER -

Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

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