While model predictive control (MPC) methods have proven their efficacy when applied to systems with safety specifications and physical limitations, their performance heavily relies on an accurate prediction model. As a consequence, a significant effort in the design of MPC controllers is dedicated to the modeling part and often requires advanced physical expertise. In order to facilitate the controller design, we present an MPC scheme supporting nonlinear learning-based prediction models, that is, data-driven models with probabilistic parameter uncertainties. A tube-based MPC formulation in combination with an additional implicit state and input constraint forces the closed-loop system to be operated in domains of sufficient model confidence, thereby ensuring asymptotic stability and constraint satisfaction at a prespecified level of probability. Furthermore, by relying on tube-based MPC concepts, the proposed learning-based MPC formulation offers a general framework for addressing different problem classes, such as economic MPC, while providing a general interface to probabilistic prediction models based, for example, on Bayesian regression or Gaussian processes. A design procedure is proposed for approximately linear systems and the efficiency of the method is illustrated using numerical examples.

中文翻译：

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基于非线性学习的模型预测控制支持状态和输入相关模型不确定性估计

虽然模型预测控制 (MPC) 方法在应用于具有安全规范和物理限制的系统时已证明其有效性，但其性能在很大程度上依赖于准确的预测模型。因此，在 MPC 控制器设计中的大量工作都致力于建模部分，并且通常需要高级物理专业知识。为了便于控制器设计，我们提出了一种支持基于非线性学习的预测模型的 MPC 方案，即具有概率参数不确定性的数据驱动模型。基于管的 MPC 公式与附加的隐式状态和输入约束相结合，迫使闭环系统在具有足够模型置信度的域中运行，从而在预先指定的概率水平上确保渐近稳定性和约束满足。此外，通过依赖基于管的 MPC 概念，所提出的基于学习的 MPC 公式提供了解决不同问题类别（例如经济 MPC）的通用框架，同时提供了基于例如贝叶斯回归的概率预测模型的通用接口或高斯过程。提出了近似线性系统的设计程序，并通过数值例子说明了该方法的效率。