Optimal Soaring with Hamilton-jacobi-bellman Equations∗

Competition glider flying, like other outdoor sports, is a game of stochastic optimization, in which mathematics and quantitative strategies have historically played an important role. We address the problem of uncertain future atmospheric conditions by constructing a nonlinear Hamilton-Jacobi-Bellman equation for the optimal speed to fly, with a free boundary describing the climb/cruise decision. This equation comes from a singular stochastic exit time control problem and involves a gradient constraint, a state constraint and a weak Dirichlet boundary condition. An accurate numerical solution requires robust monotone numerical methods. The computed results are of direct applicability for glider flight.