Stackelberg exact controllability for the Boussinesq system - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Nonlinear Differential Equations and Applications Year : 2024

Stackelberg exact controllability for the Boussinesq system

Abstract

We consider a Stackelberg control strategy applied to the Boussinesq system. More precisely, we act on this system with a hierarchy of two controls. The aim of the "leader" control is the null controllability property whereas the objective of "follower" control is to keep the state close to a given trajectory. By solving first the optimal control problem associated with the follower control, we are lead to show the null-controllability property of a system coupling a forward with a backward Boussinesq type systems. Our main result states that for an adequate weighted functional for the optimal control problem, this coupled system is locally null-controllable. To show this result, we first study the adjoint system of the linearized system and obtain a weighted observability estimate by combining several Carleman estimates and an adequate decomposition for the heat and the Stokes system.
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Dates and versions

hal-04228391 , version 1 (04-10-2023)

Identifiers

  • HAL Id : hal-04228391 , version 1

Cite

Takéo Takahashi, Luz de Teresa, Yingying Wu-Zhang. Stackelberg exact controllability for the Boussinesq system. Nonlinear Differential Equations and Applications, 2024. ⟨hal-04228391⟩
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