  Data-driven predictive control based on the fundamental lemma by Willems et
al. is frequently considered for deterministic LTI systems subject to
measurement noise. However, little has been done on data-driven stochastic
control. In this paper, we propose a data-driven stochastic predictive control
scheme for LTI systems subject to possibly unbounded additive process
disturbances. Based on a stochastic extension of the fundamental lemma and
leveraging polynomial chaos expansions, we construct a data-driven surrogate
Optimal Control Problem (OCP). Moreover, combined with an online selection
strategy of the initial condition of the OCP, we provide sufficient conditions
for recursive feasibility and for stability of the proposed data-driven
predictive control scheme. Finally, two numerical examples illustrate the
efficacy and closed-loop properties of the proposed scheme for process
disturbances governed by different distributions.
