Risk-aware stochastic control of a sailboat
Authors
- MingYi Wang, Cornell University
- Natasha Patnaik, Rice University
- Anne Somalwar, University of Pennsylvania
- Jingyi Wu, New York University
- Alexander Vladimirsky, Cornell University
Abstract
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.
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Acknowledgements
The authors would like to acknowledge Cole Miles, Roberto Ferretti, and Adriano Festa for inspiring our work. The authors also thank Mallory E. Gaspard, Cole Miles, and Elliot Cartee for providing the website template.
This work was supported in part by NSF Division of Mathematical Sciences (DMS) under Awards 1645643 and 2111522 as well as by the Air Force Office of Scientific Research under Award FA9550-22-1-0528