Data-Driven Ambiguity Sets With Probabilistic Guarantees for Dynamic Processes

Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about true probability distribution of random variables interest. This makes them a key element in data-driven robust optimization by exploiting high-confidence guarantees hedge against uncertainty. article explores construction Wasserstein dynamic scenarios, where data are collected progressively and may only reveal partial information unknown variable. For evolving according known dynamics, we leverage assimilated samples make inferences their at end sampling horizon. Under exact knowledge flow map, sufficient conditions that relate growth trajectories with rate establish reduction set size as horizon increases. Furthermore, exploitable sample history results guaranteed under errors computation when dynamics is subject bounded disturbances. Our treatment deals both full- partial-state measurements and, latter case, exploits sampled-data observability properties linear time-varying systems irregular sampling. Simulations on an unmanned aerial vehicle detection application show superior performance resulting from proposed sets.