Title: Numerical computation of singular control functions in trajectory optimization problems
Abstract: This paper considers the problem of maximizing the final velocity for a two-dimensional climb maneuver of a vehicle in atmospheric flight. The ascent of the vehicle is charaterized by a fixed initial position and a given propellant allocation. The aim is to determine the maneuver time, the throttle setting, the angle between thrust and velocity vector, and the angle of attack, such that a prescribed altitude is reached with zero path inclination and maximal final velocity. For this problem, the necessary conditions of optimal-contr ol theory are derived. It turns out that the throttle setting, which enters linearly into the state equations, in general consists of several bang-bang and singular subarcs. The problem is formulated as a boundary-value problem with switching conditions, which is solved numerically by multiple-shoo ting techniques. Solutions are presented for various values of the final altitude and various amounts of fuel. Special effort is made to give a survey of the structure of the solutions in dependence of these two parameters.
Publication Year: 1990
Publication Date: 1990-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 40
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