Optimal control for two-dimensional stochastic second grade fluids

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Chemetov, Nikolai¹  Cipriano, Fernanda^2,3 

[1] Univ Lisbon, Fac Ciencias, Dept Matemat, Lisbon, Portugal

[2] FCT UNL, CMA, Lisbon, Portugal

[3] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, Lisbon, Portugal

关键词: Stochastic second grade fluids;    Backward stochastic partial differential equations;    Stochastic optimal control;    Necessary optimality condition;   

DOI  :  10.1016/j.spa.2017.09.016

来源: Elsevier

【 摘 要 】

This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gateaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free