Stability in data-driven MPC: an inherent robustness perspective

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.

arXiv commentFinal version, accepted for presentation at the 61st IEEE Conference on Decision and Control 2022. This version contains the full proof of Theorem IV.1

References in corpus (9)

• Data-Driven Model Predictive Control with Stability and Robustness Guarantees
• Linear tracking MPC for nonlinear systems Part II: The data-driven case
• Robust stability analysis of a simple data-driven model predictive control approach
• Maximum Likelihood Estimation in Data-Driven Modeling and Control
• Robust Constraint Satisfaction in Data-Driven MPC
• Data-driven model predictive control: closed-loop guarantees and experimental results
• On the design of terminal ingredients for data-driven MPC
• Data-based Control of Feedback Linearizable Systems
• Stability in data-driven MPC: an inherent robustness perspective

Cited by in corpus (3)

• Analysis and design of model predictive control frameworks for dynamic operation -- An overview
• Stability in data-driven MPC: an inherent robustness perspective
• A Linear Parameter-Varying Approach to Data Predictive Control