Willems' fundamental lemma provides a new paradigm for data-driven system modeling and control by enabling trajectory prediction through learning of system behavior. To mitigate the influence of measurement noises, existing data-driven control approaches mainly incorporate regularization terms into the optimization problem. Although effective to some extent, their efficacy is fundamentally limited, as they do not explicitly address the probabilistic nature of noise nor do they systematically quantify inherent modeling uncertainties. This study proposes a data-driven control method based on the expectation-maximization (EM) framework. This method first establishes a probabilistic model for the offline data and performs data denoising based on a batch EM algorithm. Subsequently, a recursive EM algorithm, integrated within a receding horizon optimization framework, is used to solve the data-driven implicit model. By introducing hidden variables into the probabilistic model, the proposed method effectively addresses optimization problems involving noisy measurements in a unified probabilistic framework. Validation results from numerical simulations, the public NASA JT9D aero-engine system, and a hardware-in-the-loop platform for a two-spool turbofan engine show that, compared with the benchmark subspace predictive control method, the proposed method reduces the root-mean-square error (RMSE) by 30$\%$, 28$\%$, and 30$\%$ and increases the coefficient of determination ($\mathrm{R^{2}}$) by 45$\%$, 7$\%$, and 6$\%$, respectively, thus achieving a significant improvement in control performance.
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