Risk-aware stochastic control of a sailboat
MingYi Wang (Center for Applied Mathematics, Cornell University)
Sailboat path-planning is significantly impacted by stochastically evolving wind conditions. To navigate upwind, sailors have to perform occasional “tack-switching” maneuvers (swinging the sailboat boom to the other side, which takes time but provides access to new directions of motion). We can thus formulate sailboat path-planning as a hybrid stochastic optimal control problem. Previous studies have focused on finding a stationary/risk-neutral optimal policy that minimizes the expected time to target. In contrast, our focus is on finding robust control that maximizes the probability of reaching the target before a specified deadline/threshold. Our approach is based on stochastic dynamic programming and yields a numerical method for solving quasi-variational inequalities based on second-order Hamilton-Jacobi-Bellman PDEs with degenerate parabolicity. Our method recovers “threshold-aware” optimal policies for a range of threshold values and all starting configurations simultaneously. We use Monte-Carlo simulations to demonstrate the advantages of this “threshold-aware” approach compared to previously used stationary/risk-neutral policies. Joint work with Alex Vladimirsky and REU students (Natasha Patnaik, Anne Somalwar, and Lesley Wu).