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Distributional ambiguity sets provide quantifiable ways to characterize theuncertainty about the true probability distribution of random variables ofinterest. This makes them a key element in data-driven robust optimization byexploiting high-confidence guarantees to hedge against uncertainty. This paperexplores the construction of Wasserstein ambiguity sets in dynamic scenarioswhere data is collected progressively and may only reveal partial informationabout the unknown random variable. For random variables evolving according toknown dynamics, we leverage assimilated samples to make inferences about theirunknown distribution at the end of the sampling horizon. Under exact knowledgeof the flow map, we provide sufficient conditions that relate the growth of thetrajectories with the sampling rate to establish a reduction of the ambiguityset size as the horizon increases. Further, we characterize the exploitablesample history that results in a guaranteed reduction of ambiguity sets undererrors in the computation of the flow and when the dynamics is subject tobounded unknown disturbances. Our treatment deals with both full- andpartial-state measurements and, in the latter case, exploits the sampled-dataobservability properties of linear time-varying systems under irregularsampling. Simulations on a UAV detection application show the superiorperformance resulting from the proposed dynamic ambiguity sets.

Data-driven ambiguity sets with probabilistic guarantees for dynamic processes