Robust Stability Analysis of a Simple Data-Driven Model Predictive Control Approach

• 成果类型: Article
• 署名作者: Bongard, Joscha; Berberich, Julian; Koehler, Johannes; Allgoewer, Frank
• 署名单位: Technical University of Munich; University of Stuttgart; University of Stuttgart; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3163110
• 发表日期: 2023
• 页码: 2625-2637
• 关键词: robustness; Noise measurement; data models; trajectory; Linear systems; stability analysis; Analytical models; Data-driven control; predictive control for linear systems; uncertain systems; optimal control

摘要

In this article, 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.