Singular Perturbation Analysis of Optimal Glide

Abstract

The Singular Perturbation method is applied to determine the optimal glide trajectory in feedback form. The problem is composed of three sub-problems. The outer problem represents the classical quasi-steady-state glide, while the two inner boundary layers determine the fast dynamic phase. The timescale separation was based on the assumption that the velocity and path-angle are faster than the altitude and range, and also that the path-angle is faster than the velocity. Under these assumptions, a feedback law for the control is derived and the ensuing solution is compared to an exact one. The matching between the two is fairly good except for oscillations, which are present in the approximate solution