Data-Driven Ambiguity Sets With Probabilistic Guarantees for Dynamic Processes
Data-Driven Ambiguity Sets With Probabilistic Guarantees for Dynamic Processes
复制标题
数据驱动的歧义集为动态过程提供概率保证
DOI：
10.1109/tac.2020.3014098
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发表时间：
2019
影响因子：
6.8
通讯作者：
S. Mart'inez
中科院分区：
文献类型：
--
作者：
Dimitris Boskos;J. Cort'es;S. Mart'inez
分布模糊集提供了可量化的方法来表征感兴趣的随机变量的真实概率分布的不确定性。这使它们成为数据驱动的稳健优化的关键要素，通过利用高置信度保证来对冲不确定性。本文探讨了动态场景中 Wasserstein 模糊集的构建，其中数据是逐步收集的，并且可能仅揭示有关未知随机变量的部分信息。对于根据已知动态演化的随机变量，我们利用同化样本来推断采样范围结束时的未知分布。在准确了解流图的情况下，我们提供了将轨迹的增长与采样率联系起来的充分条件，以随着地平线的增加确定模糊集大小的减少。此外，我们描述了可利用的样本历史记录，该历史记录可以保证在流计算错误和动态受到有界未知扰动的情况下模糊集的减少。我们的处理涉及全状态和部分状态测量，并且在后一种情况下，利用不规则采样下线性时变系统的采样数据可观测性特性。对无人机检测应用的仿真显示了所提出的动态模糊度集所带来的卓越性能。
Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting high-confidence guarantees to hedge against uncertainty. This article explores the construction of Wasserstein ambiguity sets in dynamic scenarios, where data are collected progressively and may only reveal partial information about the unknown random variable. For random variables evolving according to known dynamics, we leverage assimilated samples to make inferences about their unknown distribution at the end of the sampling horizon. Under exact knowledge of the flow map, we provide sufficient conditions that relate the growth of the trajectories with the sampling rate to establish a reduction of the ambiguity set size as the horizon increases. Furthermore, we characterize the exploitable sample history that results in a guaranteed reduction of ambiguity sets under errors in the computation of the flow and when the dynamics is subject to bounded unknown disturbances. Our treatment deals with both full- and partial-state measurements and, in the latter case, exploits the sampled-data observability properties of linear time-varying systems under irregular sampling. Simulations on an unmanned aerial vehicle detection application show the superior performance resulting from the proposed dynamic ambiguity sets.
影响因子：
1
作者：
Blanchet, Jose;Kang, Yang;Murthy, Karthyek
通讯作者：
Murthy, Karthyek
影响因子：
6.8
作者：
Shen Zeng;H. Ishii;F. Allgöwer
通讯作者：
Shen Zeng;H. Ishii;F. Allgöwer