This paper describes a data-driven approach for real-time control of a physical system. Specifically, this paper focuses on the cooperative wind farm control where the objective is to maximize the total wind farm power production by using control actions as an input and measured power as an output. For real time, data-driven wind farm control, it is imperative that the optimization algorithm is able to improve a target wind farm power production by executing as small number of trial actions as possible using the wind farm power monitoring data. To achieve this goal, we develop a Bayesian ascent (BA) algorithm by incorporating into the Bayesian optimization framework a strategy that regulates the search domain, as used in the trust region method. The BA algorithm is composed of two iterative phases, namely, learning and optimization phases. In the learning phase, the BA algorithm approximates the target function using Gaussian process regression to fit the measured input and output of the target system. In the optimization phase, the BA algorithm determines the next sampling point to learn more about the target function (exploration) as well as to improve the target value (exploitation). Specifically, the sampling strategy is designed to ensure that the input is selected within a trust region to improve the target value monotonically by gradually changing the input for a target system. The results from simulation studies using an analytical wind farm power function and experimental studies using scaled wind turbines show that the BA algorithm can achieve an almost monotonic increase in the target value.