On the existence of optimal and ϵ−optimal feedback controls for stochastic second grade fluids

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Abstract

This article deals with a feedback optimal control problem for the stochastic second grade fluids. More precisely, we establish the existence of an optimal feedback control for the two-dimensional stochastic second grade fluids, with Navier-slip boundary conditions. In addition, using the Galerkin approximations, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs, showing the existence of the so-called ϵ−optimal feedback control.

Original languageEnglish
Pages (from-to)1956-1977
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume475
Issue number2
DOIs
Publication statusPublished - 15 Jul 2019

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Second Grade Fluid
Optimal Feedback Control
Feedback control
Slip Boundary Condition
Fluids
Galerkin Approximation
Costs
Optimal Control Problem
Boundary conditions
Feedback

Keywords

  • Feedback optimal control
  • Second grade fluids
  • Stochastic differential equation
  • ϵ−Optimal feedback control

Cite this

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title = "On the existence of optimal and ϵ−optimal feedback controls for stochastic second grade fluids",
abstract = "This article deals with a feedback optimal control problem for the stochastic second grade fluids. More precisely, we establish the existence of an optimal feedback control for the two-dimensional stochastic second grade fluids, with Navier-slip boundary conditions. In addition, using the Galerkin approximations, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs, showing the existence of the so-called ϵ−optimal feedback control.",
keywords = "Feedback optimal control, Second grade fluids, Stochastic differential equation, ϵ−Optimal feedback control",
author = "Fernanda Cipriano and Diogo Pereira",
note = "The authors are very grateful to the institutions Fundacao Calouste Gulbenkian, and Fundacao para a Ciencia e a Tecnologia due to the financial support. The work of D. Pereira was supported by the Fundacao Calouste Gulbenkian through the program {"}Estimulo a Investigacao 2016{"}, project {"}Monte Carlo na equagdo Hamilton-Jacobi-Bellman{"}. The work of F. Cipriano was supported by the Fundacao Calouste Gulbenkian through the project {"}Monte Carlo na equagao Hamilton-Jacobi-Bellman{"}, and Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes).",
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T1 - On the existence of optimal and ϵ−optimal feedback controls for stochastic second grade fluids

AU - Cipriano, Fernanda

AU - Pereira, Diogo

N1 - The authors are very grateful to the institutions Fundacao Calouste Gulbenkian, and Fundacao para a Ciencia e a Tecnologia due to the financial support. The work of D. Pereira was supported by the Fundacao Calouste Gulbenkian through the program "Estimulo a Investigacao 2016", project "Monte Carlo na equagdo Hamilton-Jacobi-Bellman". The work of F. Cipriano was supported by the Fundacao Calouste Gulbenkian through the project "Monte Carlo na equagao Hamilton-Jacobi-Bellman", and Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes).

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Y1 - 2019/7/15

N2 - This article deals with a feedback optimal control problem for the stochastic second grade fluids. More precisely, we establish the existence of an optimal feedback control for the two-dimensional stochastic second grade fluids, with Navier-slip boundary conditions. In addition, using the Galerkin approximations, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs, showing the existence of the so-called ϵ−optimal feedback control.

AB - This article deals with a feedback optimal control problem for the stochastic second grade fluids. More precisely, we establish the existence of an optimal feedback control for the two-dimensional stochastic second grade fluids, with Navier-slip boundary conditions. In addition, using the Galerkin approximations, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs, showing the existence of the so-called ϵ−optimal feedback control.

KW - Feedback optimal control

KW - Second grade fluids

KW - Stochastic differential equation

KW - ϵ−Optimal feedback control

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