Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Detalles Bibliográficos
Autores: Vázquez Valenzuela, Rafael, Zhang, Jing, Qi, Jie, Krstic, Miroslav
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/148434
Acceso en línea:https://hdl.handle.net/11441/148434
https://doi.org/10.1016/j.sysconle.2023.105538
Access Level:acceso abierto
Palabra clave:Partial differential equations
Spherical harmonics
Infinite-dimensional systems
Backstepping
Parabolic systems
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spelling Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional ballsVázquez Valenzuela, RafaelZhang, JingQi, JieKrstic, MiroslavPartial differential equationsSpherical harmonicsInfinite-dimensional systemsBacksteppingParabolic systemsThis is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Recently, the problem of boundary stabilization and estimation for unstable linear constant-coefficient reaction–diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However, the extension of this result to spatially-varying coefficients is far from trivial. Some early success has been achieved under simplifying conditions, such as radially-varying reaction coefficients under revolution symmetry, on a disk or a sphere. These particular cases notwithstanding, the problem remains open. The main issue is that the equations become singular in the radius; when applying the backstepping method, the same type of singularity appears in the kernel equations. Traditionally, well-posedness of these equations has been proved by transforming them into integral equations and then applying the method of successive approximations. In this case, with the resulting integral equation becoming singular, successive approximations do not easily apply. This paper takes a different route and directly addresses the kernel equations via a power series approach (in the spirit of the method of Frobenius for ordinary differential equations), finding in the process the required conditions for the radially-varying reaction (namely, analyticity and evenness) and showing the existence and convergence of the series solution. This approach provides a direct numerical method that can be readily applied, despite singularities, to both control and observer boundary design problems.ElsevierIngeniería Aeroespacial y Mecánica de FluidosTEP945: Ingeniería AeroespacialFundación Nacional de Ciencias Naturales de ChinaUniversidad de DonghuaConsejo de Becas de ChinaMinisterio de Ciencia, Innovación y Universidades (MICINN). España2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/148434https://doi.org/10.1016/j.sysconle.2023.105538reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSystems & Control Letters, 177, 105538.62173084CUSF-DH-D-2019089CSC201806630010PGC2018-100680-B-C21https://www.sciencedirect.com/science/article/pii/S0167691123000853info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1484342026-06-17T12:51:07Z
dc.title.none.fl_str_mv Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
title Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
spellingShingle Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
Vázquez Valenzuela, Rafael
Partial differential equations
Spherical harmonics
Infinite-dimensional systems
Backstepping
Parabolic systems
title_short Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
title_full Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
title_fullStr Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
title_full_unstemmed Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
title_sort Kernel well-posedness and computation by power series in backstepping output feedback for radially-dependent reaction–diffusion PDEs on multidimensional balls
dc.creator.none.fl_str_mv Vázquez Valenzuela, Rafael
Zhang, Jing
Qi, Jie
Krstic, Miroslav
author Vázquez Valenzuela, Rafael
author_facet Vázquez Valenzuela, Rafael
Zhang, Jing
Qi, Jie
Krstic, Miroslav
author_role author
author2 Zhang, Jing
Qi, Jie
Krstic, Miroslav
author2_role author
author
author
dc.contributor.none.fl_str_mv Ingeniería Aeroespacial y Mecánica de Fluidos
TEP945: Ingeniería Aeroespacial
Fundación Nacional de Ciencias Naturales de China
Universidad de Donghua
Consejo de Becas de China
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
dc.subject.none.fl_str_mv Partial differential equations
Spherical harmonics
Infinite-dimensional systems
Backstepping
Parabolic systems
topic Partial differential equations
Spherical harmonics
Infinite-dimensional systems
Backstepping
Parabolic systems
description This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/148434
https://doi.org/10.1016/j.sysconle.2023.105538
url https://hdl.handle.net/11441/148434
https://doi.org/10.1016/j.sysconle.2023.105538
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Systems & Control Letters, 177, 105538.
62173084
CUSF-DH-D-2019089
CSC201806630010
PGC2018-100680-B-C21
https://www.sciencedirect.com/science/article/pii/S0167691123000853
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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