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arXiv · 2103.00851

Robust stability analysis of a simple data-driven model predictive control approach

Joscha Bongard·Julian Berberich·Johannes Köhler·Frank Allgöwer
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Abstract

In this paper, we provide a theoretical analysis of closed-loop properties of a simple data-driven model predictive control (MPC) scheme. The formulation does not involve any terminal ingredients, thus allowing for a simple implementation without (potential) feasibility issues. The proposed approach relies on an implicit description of linear time-invariant systems based on behavioral systems theory, which only requires one input-output trajectory of an unknown system. For the nominal case with noise-free data, we prove that the data-driven MPC scheme ensures exponential stability for the closed loop if the prediction horizon is sufficiently long. Moreover, we analyze the robust data-driven MPC scheme for noisy output measurements for which we prove closed-loop practical exponential stability. The advantages of the presented approach are illustrated with a numerical example.

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Joscha Bongard, Julian Berberich, Johannes Köhler, Frank Allgöwer. 2021-03-01. Robust stability analysis of a simple data-driven model predictive control approach. https://doi.org/10.1109/tac.2022.3163110

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