Model Predictive Control for Linear Uncertain Systems Using Integral Quadratic Constraints

• 成果类型: Article
• 署名作者: Schwenkel, Lukas; Koehler, Johannes; Mueller, Matthias A. A.; Allgoewer, Frank
• 署名单位: University of Stuttgart; Swiss Federal Institutes of Technology Domain; ETH Zurich; Leibniz University Hannover
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3171410
• 发表日期: 2023
• 页码: 355-368
• 关键词: Integral quadratic constraints (IQCs); predictive control for linear systems; Robust control; uncertain systems

摘要

In this work, we propose a tube-based model predictive control (MPC) scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $\rho$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scaling parameter for the tube size. We prove that this method achieves robust constraint satisfaction and input-to-state stability despite dynamic uncertainties and additive bounded disturbances. A numerical example demonstrates the reduced conservatism of this IQC approach compared to state-of-the-art robust MPC approaches for dynamic uncertainties.