时变线性系的高置信度数据驱动模糊集
High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems
摘要：
本文建立了Wasserstein模糊集的动态随机变量的未知概率分布利用噪声部分状态观测。所构造的模糊度集包含具有可量化概率的数据的真实分布，并且可以用来制定具有样本外保证的鲁棒随机最优化问题。我们假设随机变量在不确定的初始条件和动态下在离散时间内演化，并且可以获得噪声部分测量。所有随机元具有未知的概率分布，并且我们使用来自该过程的多个实现的若干输出样本来推断状态向量的分布。为此，我们利用一个观察者来估计每个独立实现的状态，并利用结果来构建模糊集。我们说明了我们的结果在一个经济调度问题，涉及分布式能源调度没有直接控制。
英文摘要：
This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out-of-sample guarantees. We assume the random variable evolves in discrete time under uncertain initial conditions and dynamics, and that noisy partial measurements are available. All random elements have unknown probability distributions and we make inferences about the distribution of the state vector using several output samples from multiple realizations of the process. To this end, we leverage an observer to estimate the state of each independent realization and exploit the outcome to construct the ambiguity sets. We illustrate our results in an economic dispatch problem involving distributed energy resources over which the scheduler has no direct control.
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