Optimal Soaring via Hamilton-Jacobi-Bellman Equations

Optimal Control, Applications and Methods, Forthcoming.

28 Pages Posted: 22 Feb 2014 Last revised: 3 Apr 2014

See all articles by Robert Almgren

Robert Almgren

University of Toronto - Department of Mathematics

Agnes Tourin

NYU Tandon - Department of Finance and Risk Engineering

Date Written: February 20, 2014

Abstract

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 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.

Keywords: Hamilton-Jacobi equations; glider flying; Variational Inequalities; stochastic control; finite difference; monotone approximation

JEL Classification: C61,C63

Suggested Citation

Almgren, Robert and Tourin, Agnes, Optimal Soaring via Hamilton-Jacobi-Bellman Equations (February 20, 2014). Optimal Control, Applications and Methods, Forthcoming., Available at SSRN: https://ssrn.com/abstract=2399214 or http://dx.doi.org/10.2139/ssrn.2399214

Robert Almgren

University of Toronto - Department of Mathematics ( email )

Toronto, Ontario M5S 3G3
Canada

Agnes Tourin (Contact Author)

NYU Tandon - Department of Finance and Risk Engineering ( email )

NY
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
107
Abstract Views
563
rank
279,143
PlumX Metrics