Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

We present a novel methodology for designing output-feedback backstepping bilateral boundary controllers for an unstable 1D diffusion-reaction partial differential equation (PDE) with spatially varying reaction. Using folding transforms the parabolic PDE into a 2 × 2 coupled PDE system with coupling...

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Detalles Bibliográficos
Autores: Chen, Stephen, Vázquez Valenzuela, Rafael, Krstic, Miroslav
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/137783
Acceso en línea:https://hdl.handle.net/11441/137783
https://doi.org/10.1109/TAC.2021.3080503
Access Level:acceso abierto
Palabra clave:Backstepping
Distributed parameter systems
Multiple input
Partial differential equations (PDE)
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spelling Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDEChen, StephenVázquez Valenzuela, RafaelKrstic, MiroslavBacksteppingDistributed parameter systemsMultiple inputPartial differential equations (PDE)We present a novel methodology for designing output-feedback backstepping bilateral boundary controllers for an unstable 1D diffusion-reaction partial differential equation (PDE) with spatially varying reaction. Using folding transforms the parabolic PDE into a 2 × 2 coupled PDE system with coupling through compatibility conditions. We apply a two-tiered backstepping approach, where the invertibility of the transformations guarantees the statefeedback controllers exponentially stabilize the trivial solution of the PDE system. A state observer is also designed for two collocated measurements at an arbitrary interior point, generating exponentially stable state estimates. The output feedback control law is formulated by composing the independently designed state-feedback controller with the observer, and the resulting dynamic feedback is shown to stabilize the trivial solution. Some numerical analysis on how the selection of these points affect the responses of the controller and observer are discussed, with simulations illustrating various choices of folding points and their effect on the stabilization in different performance indexes.Institute of Electrical and Electronics Engineers Inc.Ingeniería Aeroespacial y Mecánica de Fluidos2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/137783https://doi.org/10.1109/TAC.2021.3080503reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésIEEE Transactions on Automatic Control, 67 (5), 2389-2404.https://ieeexplore.ieee.org/abstract/document/9431688info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1377832026-06-17T12:51:07Z
dc.title.none.fl_str_mv Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
title Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
spellingShingle Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
Chen, Stephen
Backstepping
Distributed parameter systems
Multiple input
Partial differential equations (PDE)
title_short Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
title_full Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
title_fullStr Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
title_full_unstemmed Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
title_sort Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE
dc.creator.none.fl_str_mv Chen, Stephen
Vázquez Valenzuela, Rafael
Krstic, Miroslav
author Chen, Stephen
author_facet Chen, Stephen
Vázquez Valenzuela, Rafael
Krstic, Miroslav
author_role author
author2 Vázquez Valenzuela, Rafael
Krstic, Miroslav
author2_role author
author
dc.contributor.none.fl_str_mv Ingeniería Aeroespacial y Mecánica de Fluidos
dc.subject.none.fl_str_mv Backstepping
Distributed parameter systems
Multiple input
Partial differential equations (PDE)
topic Backstepping
Distributed parameter systems
Multiple input
Partial differential equations (PDE)
description We present a novel methodology for designing output-feedback backstepping bilateral boundary controllers for an unstable 1D diffusion-reaction partial differential equation (PDE) with spatially varying reaction. Using folding transforms the parabolic PDE into a 2 × 2 coupled PDE system with coupling through compatibility conditions. We apply a two-tiered backstepping approach, where the invertibility of the transformations guarantees the statefeedback controllers exponentially stabilize the trivial solution of the PDE system. A state observer is also designed for two collocated measurements at an arbitrary interior point, generating exponentially stable state estimates. The output feedback control law is formulated by composing the independently designed state-feedback controller with the observer, and the resulting dynamic feedback is shown to stabilize the trivial solution. Some numerical analysis on how the selection of these points affect the responses of the controller and observer are discussed, with simulations illustrating various choices of folding points and their effect on the stabilization in different performance indexes.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/137783
https://doi.org/10.1109/TAC.2021.3080503
url https://hdl.handle.net/11441/137783
https://doi.org/10.1109/TAC.2021.3080503
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv IEEE Transactions on Automatic Control, 67 (5), 2389-2404.
https://ieeexplore.ieee.org/abstract/document/9431688
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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