On Data-Driven Stochastic Output-Feedback Predictive Control

Recently, the fundamental lemma by Willems et al. has seen frequent use for the design of data-driven output-feedback predictive control. However, the majority of existing results considers deterministic Linear Time-Invariant (LTI) systems with or without measurement noise. In this paper, we analyze data-driven output-feedback predictive control of stochastic LTI systems with respect to closed-loop guarantees on recursive feasibility, performance, and stability. Based on a stochastic variant of the fundamental lemma and leveraging polynomial chaos expansions, we construct a data-driven Optimal Control Problem (OCP) that allows the propagation of uncertainties over finite prediction horizons. The OCP includes a terminal cost and terminal constraints expressed in predicted inputs and outputs. Combined with a selection strategy of initial conditions, we prove sufficient conditions for recursive feasibility and for the practical stability of the proposed scheme. A numerical example illustrates the efficacy of the proposed scheme.