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The paper investigates data-driven output-feedback predictive control oflinear systems subject to stochastic disturbances. The scheme relies on therecursive solution of a suitable data-driven reformulation of a stochasticOptimal Control Problem (OCP), which allows for forward prediction andoptimization of statistical distributions of inputs and outputs. Our approachavoids the use of parametric system models. Instead it is based on previouslyrecorded data using a recently proposed stochastic variant of Willems'fundamental lemma. The stochastic variant of the lemma is applicable to a largeclass of linear dynamics subject to stochastic disturbances of Gaussian andnon-Gaussian nature. To ensure recursive feasibility, the initial condition ofthe OCP -- which consists of information about past inputs and outputs -- isconsidered as an extra decision variable of the OCP. We provide sufficientconditions for recursive feasibility and closed-loop practical stability of theproposed scheme as well as performance bounds. Finally, a numerical exampleillustrates the efficacy and closed-loop properties of the proposed scheme.

Data-driven Stochastic Output-Feedback Predictive Control: Recursive Feasibility through Interpolated Initial Conditions