On the minimum time optimal control problem of an aircraft in its climbing phase

Abstract

In this article, the minimum time optimal control problem of an aircraft in its climbing phase is studied.First, a reduction of the initial dynamics into a three dimensional single-input system with a linear de-pendence with respect to the control is performed. This reduced system is then studied using geometriccontrol techniques. In particular, the maximum principle leads to describe a multi-point boundary valueproblem which is solved by indirect methods. These methods are the implementation of the maximumprinciple and are initialized by direct methods. We check that the extremal solution of the boundary valueproblem satisfies necessary and sufficient conditions of optimality. From this reference case and consider-ing small-time optimal trajectories, we give a local classification with respect to the initial mass and finalvelocity of BC-extremals for the climbing phase.