Optimal Soaring via Hamilton-Jacobi-Bellman Equations

Robert Almgren, Agnes Tourin
2014 Social Science Research Network  
Competition glider flying 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. We consider two different forms of knowledge about future atmospheric conditions, the first in which the pilot has complete
more » ... lot has complete foreknowledge and the second in which the state of the atmosphere is a Markov process discovered by flying through it. We compute an accurate numerical solution by designing a robust monotone finite difference method. The results obtained are of direct applicability for glider flight.
doi:10.2139/ssrn.2399214 fatcat:alaj2asxvzgd7nzorfose25h6q