This article proposes a novel distributionally robust optimization (DRO)‐based soft‐constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state‐space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first‐order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO‐based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi‐stage scenario based stochastic MPC.

中文翻译：

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基于数据驱动的分布鲁棒优化的软约束模型预测控制

本文提出了一种新颖的基于分布鲁棒优化（DRO）的软约束模型预测控制（MPC）框架，以明确对冲线性状态空间系统中未知的外部输入项。在没有先验知识的确切不确定性分布的情况下，该框架与使用机器学习构建的，包含一阶矩信息的提升歧义集一起工作。通过采用线性性能度量并针对提升的支持集稳健地考虑输入和状态约束，将基于DRO的MPC重新构造为稳健的优化问题。约束被软化以确保递归的可行性。进一步讨论了关于最优性，可行性和稳定性的理论结果。