论文标题
数据驱动的MPC中的稳定性：固有的鲁棒性观点
Stability in data-driven MPC: an inherent robustness perspective
论文作者
论文摘要
基于Willems的基本引理的数据驱动模型预测控制（DD-MPC）近年来受到了很多关注，从而可以基于隐式数据依赖性系统描述直接控制系统。文献包含许多成功的实用应用以及闭环稳定性和鲁棒性的理论结果。在本文中，我们提供了DD-MPC的教程介绍，用于未知的线性时间不变（LTI）系统，重点是（稳健）闭环稳定性。我们首先解决了无噪声数据的方案，为此我们提供了具有终端等效约束的DD-MPC方案，并得出了闭环属性。如果有嘈杂的数据，我们引入了一种简单而强大的方法，通过结合DD-MPC W.R.T.的连续性来分析DD-MPC的稳健稳定性。具有基于模型的MPC的固有稳健性，即名义MPC W.R.T.的稳健性，即小型干扰。此外，我们讨论提供的证明技术如何允许使用嘈杂数据显示各种DD-MPC方案的闭环稳定性，只要基于相应的基于模型的MPC本质上是强大的。
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.
