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

Fernanda Cipriano; Diogo Pereira

doi:10.1016/j.jmaa.2019.03.064

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

Fernanda Cipriano, Diogo Pereira

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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 language	English
Pages (from-to)	1956-1977
Number of pages	22
Journal	Journal of Mathematical Analysis and Applications
Volume	475
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2019.03.064
Publication status	Published - 15 Jul 2019

Keywords

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

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10.1016/j.jmaa.2019.03.064Licence: CC BY-NC-ND

On the existence of optimalAccepted author manuscript, 365 KBLicence: CC BY-NC-ND

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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).",

year = "2019",

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doi = "10.1016/j.jmaa.2019.03.064",

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TY - JOUR

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).

PY - 2019/7/15

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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DO - 10.1016/j.jmaa.2019.03.064

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SN - 0022-247X

VL - 475

SP - 1956

EP - 1977

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

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Keywords

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