Dynamic polynomial stabilization of a 1D wave equation

Lassi Paunonen; Jukka-Pekka Humaloja

doi:10.1137/1.9781611975758.16

Dynamic polynomial stabilization of a 1D wave equation

Lassi Paunonen, Jukka-Pekka Humaloja

Computing Sciences

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

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Abstract

We study observer-based dynamic stabilization of a one-dimensional wave equation with boundary control and distributed observation. The control system we consider is exponentially stabilizable but not exponentially detectable. Consequently, exponential energy decay is not achievable with dynamic output feedback. As our main result we design an observer-based controller which achieves rational decay of energy for a class of initial conditions. The controller design relies on helpful results on polynomial stability of semigroups generated by block operator matrices.

Original language	English
Title of host publication	2019 Proceedings of the Conference on Control and its Applications
Editors	William S. Levine, Richard Stockbridge
Publisher	SIAM, Society for Industrial and Applied Mathematics
Pages	105-109
Number of pages	5
ISBN (Electronic)	978-1-61197-575-8
DOIs	https://doi.org/10.1137/1.9781611975758.16
Publication status	Published - 2019
Publication type	A4 Article in conference proceedings
Event	SIAM Conference on Control and its Applications - Chengdu, China Duration: 19 Jun 2019 → 21 Jun 2019

Conference

Conference	SIAM Conference on Control and its Applications
Country/Territory	China
City	Chengdu
Period	19/06/19 → 21/06/19

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10.1137/1.9781611975758.16

Dynamic polynomial stabilization
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title = "Dynamic polynomial stabilization of a 1D wave equation",

abstract = "We study observer-based dynamic stabilization of a one-dimensional wave equation with boundary control and distributed observation. The control system we consider is exponentially stabilizable but not exponentially detectable. Consequently, exponential energy decay is not achievable with dynamic output feedback. As our main result we design an observer-based controller which achieves rational decay of energy for a class of initial conditions. The controller design relies on helpful results on polynomial stability of semigroups generated by block operator matrices.",

author = "Lassi Paunonen and Jukka-Pekka Humaloja",

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editor = "Levine, {William S.} and Richard Stockbridge",

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note = "SIAM Conference on Control and its Applications ; Conference date: 19-06-2019 Through 21-06-2019",

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Paunonen, L & Humaloja, J-P 2019, Dynamic polynomial stabilization of a 1D wave equation. in WS Levine & R Stockbridge (eds), 2019 Proceedings of the Conference on Control and its Applications. SIAM, Society for Industrial and Applied Mathematics, pp. 105-109, SIAM Conference on Control and its Applications , Chengdu, China, 19/06/19. https://doi.org/10.1137/1.9781611975758.16

Dynamic polynomial stabilization of a 1D wave equation. / Paunonen, Lassi; Humaloja, Jukka-Pekka.
2019 Proceedings of the Conference on Control and its Applications. ed. / William S. Levine; Richard Stockbridge. SIAM, Society for Industrial and Applied Mathematics, 2019. p. 105-109.

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

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AU - Humaloja, Jukka-Pekka

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N2 - We study observer-based dynamic stabilization of a one-dimensional wave equation with boundary control and distributed observation. The control system we consider is exponentially stabilizable but not exponentially detectable. Consequently, exponential energy decay is not achievable with dynamic output feedback. As our main result we design an observer-based controller which achieves rational decay of energy for a class of initial conditions. The controller design relies on helpful results on polynomial stability of semigroups generated by block operator matrices.

AB - We study observer-based dynamic stabilization of a one-dimensional wave equation with boundary control and distributed observation. The control system we consider is exponentially stabilizable but not exponentially detectable. Consequently, exponential energy decay is not achievable with dynamic output feedback. As our main result we design an observer-based controller which achieves rational decay of energy for a class of initial conditions. The controller design relies on helpful results on polynomial stability of semigroups generated by block operator matrices.

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DO - 10.1137/1.9781611975758.16

M3 - Conference contribution

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BT - 2019 Proceedings of the Conference on Control and its Applications

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PB - SIAM, Society for Industrial and Applied Mathematics

T2 - SIAM Conference on Control and its Applications

Y2 - 19 June 2019 through 21 June 2019

ER -

Dynamic polynomial stabilization of a 1D wave equation

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