On the Inherent Distributional Robustness of Stochastic and Nominal Model Predictive Control
On the Inherent Distributional Robustness of Stochastic and Nominal Model Predictive Control
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DOI：
10.1109/tac.2023.3273420
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发表时间：
2024-02
影响因子：
6.8
通讯作者：
Robert D. McAllister;J. Rawlings
中科院分区：
文献类型：
--
作者：
Robert D. McAllister;J. Rawlings
我们通过Wasserstein度量定义了分布鲁棒性的概念，用于闭环系统，遇到用于构建控制器的干扰分布中的错误。然后，我们为随机模型预测控制（SMPC）建立了足够的条件，以满足分布鲁棒性的这种定义，并为SMPC的经济应用建立了类似的分布鲁棒性概念。这些结果解决了错误或未建模的干扰，证明了场景优化的功效，作为近似和解决SMPC问题的手段，并统一了随机模型和名义模型预测控制的鲁棒性描述。闭环系统的分布鲁棒性的定义是一般的，可以应用于其他随机最佳控制算法，并有可能是分布稳健控制的发展场。
We define a notion of distributional robustness, via the Wasserstein metric, for closed-loop systems subject to errors in the disturbance distribution used to construct the controller. We then establish sufficient conditions for stochastic model predictive control (SMPC) to satisfy this definition of distributional robustness and establish a similar notion of distributional robustness for economic applications of SMPC. These results address incorrectly or unmodeled disturbances, demonstrate the efficacy of scenario optimization as a means to approximate and solve the SMPC problem, and unify the descriptions of robustness for stochastic and nominal model predictive control. This definition of distributional robustness for closed-loop systems is general and can be applied to other stochastic optimal control algorithms and, potentially, the developing field of distributionally robust control.