Stability in data-driven MPC: an inherent robustness perspective
Julian Berberich, Johannes Köhler, Matthias A. Müller, Frank Allgöwer
TL;DR
The paper addresses stability and robustness of data-driven MPC (DD-MPC) for unknown LTI systems using Willems' Fundamental Lemma. It introduces a two-step robustness approach: first, it shows that data noise can be translated into an input disturbance for a nominal model-based MPC, and second, it leverages the inherent robustness of that nominal MPC to achieve stability; this is extended to noisy data via a robust, slack-based DD-MPC formulation and a multi-step implementation that preserves recursive feasibility and yields practical exponential stability. The main contributions include a continuity bound linking data noise to input deviations, a proof that inherent robustness of model-based MPC transfers to DD-MPC under mild conditions, and a general, transferable framework that applies to a broad class of DD-MPC schemes with terminal constraints. The results bridge DD-MPC with classical MPC robustness theory, enabling reliable data-driven control under measurement noise and offering guidance for future quantification of stability regions and extensions beyond terminal constraints.
Abstract
Data-driven model predictive control (DD-MPC) based on Willems' Fundamental Lemma has received much attention in recent years, allowing to control systems directly based on an implicit data-dependent system description. The literature contains many successful practical applications as well as theoretical results on closed-loop stability and robustness. In this paper, we provide a tutorial introduction to DD-MPC for unknown linear time-invariant (LTI) systems with focus on (robust) closed-loop stability. We first address the scenario of noise-free data, for which we present a DD-MPC scheme with terminal equality constraints and derive closed-loop properties. In case of noisy data, we introduce a simple yet powerful approach to analyze robust stability of DD-MPC by combining continuity of DD-MPC w.r.t. noise with inherent robustness of model-based MPC, i.e., robustness of nominal MPC w.r.t. small disturbances. Moreover, we discuss how the presented proof technique allows to show closed-loop stability of a variety of DD-MPC schemes with noisy data, as long as the corresponding model-based MPC is inherently robust.