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arXiv · 2211.17074

On Data-Driven Stochastic Output-Feedback Predictive Control

Guanru Pan·Ruchuan Ou·Timm Faulwasser
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Abstract

The fundamental lemma by Jan C. Willems and co-authors enables the representation of all input-output trajectories of a linear time-invariant 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 paper presents a data-driven output-feedback predictive control scheme for stochastic Linear Time-Invariant (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.

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Guanru Pan, Ruchuan Ou, Timm Faulwasser. 2022-11-30. On Data-Driven Stochastic Output-Feedback Predictive Control. https://arxiv.org/abs/2211.17074

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