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A penalty approach to the infinite horizon LQR optimal control problem for the linearized Boussinesq system

hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorLE BALC’H, Kévin
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTUCSNAK, Marius
dc.date.accessioned2024-04-04T02:46:54Z
dc.date.available2024-04-04T02:46:54Z
dc.date.issued2021
dc.identifier.issn1292-8119
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191596
dc.description.abstractEnIn this paper, we consider the infinite time horizon LQR optimal control problem for the linearized Boussinesq system. The goal is to justify the approximation by penalization of the free divergence condition in this context. We establish convergence results for optimal controls, optimal solutions and Riccati operators when the penalization parameter goes to zero. These results are obtained under two different assumptions. The first one treats the linearization around a sufficiently small stationary state and an arbitrary control operator (possibly of finite rank), while the second one does no longer require the smallness of the stationary state but requires to consider controls distributed in a subdomain and depending on the space variable.
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisherEDP Sciences
dc.subject.enLinear quadratic optimal control
dc.subject.enRiccati theory
dc.subject.enBoussinesq system
dc.subject.enpenalty method
dc.subject.encontrollability
dc.title.enA penalty approach to the infinite horizon LQR optimal control problem for the linearized Boussinesq system
dc.typeArticle de revue
dc.identifier.doi10.1051/cocv/2021008
dc.subject.halMathématiques [math]
bordeaux.journalESAIM: Control, Optimisation and Calculus of Variations
bordeaux.page17
bordeaux.volume27
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03177150
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03177150v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=ESAIM:%20Control,%20Optimisation%20and%20Calculus%20of%20Variations&rft.date=2021&rft.volume=27&rft.spage=17&rft.epage=17&rft.eissn=1292-8119&rft.issn=1292-8119&rft.au=LE%20BALC%E2%80%99H,%20K%C3%A9vin&TUCSNAK,%20Marius&rft.genre=article


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