On Data-Driven Stochastic Output-Feedback Predictive Control

The fundamental lemma by J. C. Willems and coauthors enables the representation of all input–output trajectories of a linear time-invariant (LTI) system by measured input–output data. This result has proven to be pivotal for data-driven control. Building on a stochastic variant of the fundamental lemma, this article presents a data-driven output-feedback predictive control scheme for stochastic LTI systems. The considered LTI systems are subject to non-Gaussian 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.