Modern wind farm control (WFC) methods in the literature typically rely on a surrogate model of the farm dynamics that is computationally inexpensive to enable real-time computations. As it is very difficult to model all the relevant wind farm dynamics accurately, a closed-loop approach is a prerequisite for reliable WFC. As one of the few in its field, this paper showcases a closed-loop wind farm control solution, which leverages a steady-state surrogate model and Bayesian Optimization to maximize the wind-farm-wide power production. The estimated quantities are the time-averaged ambient wind direction, wind speed and turbulence intensity. This solution is evaluated for a wind farm with nine 10 MW wind turbines in large-eddy simulation, showing a time-averaged power gain of 4.4%. This is the first WFC algorithm that is tested for wind turbines of such scale in high fidelity.