Robust stability analysis of a simple data-driven model predictive control approach
Joscha Bongard, Julian Berberich, Johannes Köhler, Frank Allgöwer
TL;DR
The article addresses stability and robustness in a simple data-driven MPC that relies on a single input-output trajectory and requires no model knowledge. By leveraging the Willems Fundamental Lemma and an extended state-space formulation, the authors prove exponential stability for nominal data with a sufficiently long horizon and establish practical exponential stability under bounded noise with a carefully designed robust MPC. The approach avoids terminal constraints, improving robustness and numerical properties relative to terminal-constraint MPC methods, and is validated on a linearized CSTR example where it outperforms a terminal-equality constrained baseline. This work provides rigorous closed-loop guarantees for direct data-driven MPC and offers guidance on horizon lengths and noise handling for practical deployments.
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.