Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.08858 |
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Sommario:
- Probabilistic prediction of stochastic dynamical systems (SDSs) aims to accurately predict the conditional probability distributions of future states. However, accurate probabilistic predictions tightly hinge on accurate distributional information from a nominal model, which is hardly available in practice. To address this issue, we propose a novel functional-maximin-based distributionally robust probabilistic prediction (DRPP) framework. In this framework, one can design probabilistic predictors that have worst-case performance guarantees over a pre-defined ambiguity set of SDSs. Nevertheless, DRPP requires optimizing over the space of probability measures with density functions with respect to the Lebesgue measure, which is generally intractable. We develop a methodology that equivalently transforms the original maximin from function spaces to Euclidean spaces. Although it remains intractable to seek a global optimal solution, two suboptimal solutions are derived. By relaxing the constraints on the ambiguity set, we obtain a suboptimal predictor called Noise-DRPP. Relaxing the constraints on the predictor yields another suboptimal predictor, Eig-DRPP. Moreover, optimality gaps between the proposed predictors and the global optimal predictor are derived. Finally, we conduct elaborate numerical simulations to compare the performance of different predictors under different SDSs.