On Using Feedback Control to Contend with Nature’s Randomness
On Using Feedback Control to Contend with Nature’s Randomness
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DOI：
10.1021/acs.iecr.2c02970
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Robert D. McAllister;J. Rawlings
中科院分区：
文献类型：
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作者：
Robert D. McAllister;J. Rawlings
概率分布经常被用来描述自然界的随机性。在随机模型预测控制(SMPC)中，扰动是用随机优化问题中的概率分布来描述的，以构造反馈控制律。虽然这些概率分布很强大，但它们本身也受到自己类型的不确定性的影响，通常被称为分布不确定性。在这项工作中，我们建立了SMPC，在适当的假设下，提供了对这种分布不确定性的非零鲁棒裕度。反馈和仔细的算法设计提供了这种固有的分布稳健性。通过一个小例子，我们演示了这一结果对于错误建模、样本外甚至未建模的干扰的影响。这一结果还涵盖了基于情景的随机最优控制问题的近似，并统一了标称模型预测控制和随机模型预测控制的鲁棒性描述。
Probability distributions are often used to characterize the randomness of nature. In stochastic model predictive control (SMPC), disturbances are described by a probability distribution that is used within a stochastic optimization problem to construct a feedback control law. While powerful, these probability distributions are themselves subject to their own type of uncertainty, often called distributional uncertainty. In this work, we establish that SMPC, under suitable assumptions, provides a nonzero margin of robustness to this distributional uncertainty. This inherent distributional robustness is afforded by feedback and careful algorithm design. Through a small example, we demonstrate the implications of this result for incorrectly modeled, out-of-sample, and even unmodeled disturbances. This result also covers scenario-based approximations of stochastic optimal control problems and unifies the description of robustness for nominal and stochastic model predictive control.