Stability in data-driven MPC: an inherent robustness perspective

TL;DR

This paper explores the inherent robustness of data-driven model predictive control (DD-MPC) for unknown LTI systems, emphasizing stability analysis under noise and demonstrating how robustness properties transfer from model-based MPC.

Contribution

It introduces a stability analysis framework for DD-MPC that accounts for noisy data by leveraging the robustness of traditional MPC, providing new insights into its stability guarantees.

Findings

Robust stability of DD-MPC can be analyzed using continuity w.r.t. noise.

Inherent robustness of model-based MPC extends to DD-MPC schemes.

The approach applies to various DD-MPC schemes with noisy data.

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.