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

Olivier Cots (1, 2) , Patrick Delpy (3) , Joseph Gergaud (1, 2) , Damien Goubinat (1)

1 IRIT-APO - Algorithmes Parallèles et Optimisation
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 Thales Avionics

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.

Mots clés: Time optimal control problem; Aircraft climbing phase

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Olivier Cots, Patrick Delpy, Joseph Gergaud, Damien Goubinat. On the minimum time optimal control problem of an aircraft in its climbing phase. 7th Euporean Conferencer for Aeronautics and Aerospace Sciences (EUCASS 2017), Jul 2017, Milan, Italy. pp.1-14. ⟨hal-02559831⟩