  The fundamental lemma introduced in the context of behavioral systems theory
by Jan C. Willems and co-authors is of tremendous relevance for data-driven
control. Building on a stochastic variant of the fundamental lemma, this paper
presents a data-driven output-feedback predictive control scheme for stochastic
Linear Time-Invariant (LTI) systems. The considered LTI systems are subject to
unmeasured disturbances about which only information about their first two
moments is known. Leveraging polynomial chaos expansions, the proposed scheme
is centered around a data-driven stochastic Optimal Control Problem (OCP).
Through tailored online design of initial conditions, we provide sufficient
conditions for the recursive feasibility of the proposed output-feedback scheme
based on a data-driven design of the terminal ingredients of the OCP.
Furthermore, we provide a robustness analysis of the closed-loop performance. A
numerical example illustrates the efficacy of the proposed scheme.
