  In this paper, we study some controllability and observability problems for
stochastic systems coupling fourth- and second-order parabolic equations. The
main goal is to control both equations with only one controller localized on
the drift of the fourth-order equation. We analyze two cases: on one hand, we
study the controllability of a linear backward system where the couplings are
made only through first-order terms. The key point is to use suitable Carleman
estimates for the heat equation and the fourth-order operator with the same
weight to deduce an observability inequality for the adjoint system. On the
other hand, we study the controllability of a simplified nonlinear coupled
model of forward equations. This case, which is well-known to be harder to
solve, follows a methodology that has been introduced recently and relies on an
adaptation of the well-known source term method in the stochastic setting
together with a truncation procedure. This approach gives a new concept of
controllability for stochastic systems.

Optimization and Control