Risk-aware stochastic control of a sailboat
| Autor: | Wang, MingYi, Patnaik, Natasha, Somalwar, Anne, Wu, Jingyi, Vladimirsky, Alexander |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Sailboat path-planning is a natural hybrid control problem (due to continuous steering and occasional "tack-switching" maneuvers), with the actual path-to-target greatly affected by stochastically evolving wind conditions. Previous studies have focused on finding risk-neutral policies that minimize the expected time of arrival. In contrast, we present a robust control approach, which maximizes the probability of arriving before a specified deadline/threshold. Our numerical method recovers the optimal risk-aware (and threshold-specific) policies for all initial sailboat positions and a broad range of thresholds simultaneously. This is accomplished by solving two quasi-variational inequalities based on second-order Hamilton-Jacobi-Bellman (HJB) PDEs with degenerate parabolicity. Monte-Carlo simulations show that risk-awareness in sailing is particularly useful when a carefully calculated bet on the evolving wind direction might yield a reduction in the number of tack-switches. Comment: 6 pages; 4 figures |
| Databáze: | arXiv |
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