  This work aims to control the dynamics of certain non-Newtonian fluids in a
bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener
noise, the control acts as a predictable distributed random force, and the goal
is to achieve a predefined velocity profile under a minimal cost. Due to the
strong nonlinearity of the stochastic state equations, strong solutions are
available just locally in time, and the cost functional includes an appropriate
stopping time. First, we show the existence of an optimal pair. Then,we show
that the solution of the stochastic forward linearized equation coincides with
the G\^ateaux derivative of the control-to-state mapping, after establishing
some stability results. Next, we analyse the backward stochastic adjoint
equation; where the uniqueness of solution holds only when $d=2$. Finally, we
establish a duality relation and deduce the necessary optimality conditions.
