  In this paper, we study a boundary control problem associated to the
stationary Rayleigh-B\'enard-Marangoni (RBM) system in presence of controls for
the velocity and the temperature on parts of the boundary. We analyze the
existence, uniqueness and regularity of weak solutions for the stationary RBM
system in polyhedral domains of $\mathbb{R}^3,$ and then, we prove the
existence of the optimal solution. By using the Theorem of Lagrange
multipliers, we derive an optimality system. We also give a second-order
sufficient optimality condition and we establish a result of uniqueness of the
optimal solution.
