LE BALC’H, Kévin; TUCSNAK, Marius

doi:10.1051/cocv/2021008

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LE BALC’H, Kévin
Institut de Recherche Mathématique de Rennes [IRMAR]

TUCSNAK, Marius
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

ESAIM: Control, Optimisation and Calculus of Variations. 2021, vol. 27, p. 17

EDP Sciences

Résumé en anglais

In 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.< Réduire

Mots clés en anglais

Linear quadratic optimal control

Riccati theory

Boussinesq system

penalty method

controllability

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191596

DOI

http://dx.doi.org/10.1051/cocv/2021008

Project ANR

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251