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On the existence of optimal and \(\epsilon\)-optimal feedback controls for stochastic second grade fluids. (English) Zbl 1415.93290

Summary: 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 \(\epsilon\)-optimal feedback control.

MSC:

93E20 Optimal stochastic control
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
93B52 Feedback control
93E03 Stochastic systems in control theory (general)
93C20 Control/observation systems governed by partial differential equations
76M35 Stochastic analysis applied to problems in fluid mechanics
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