| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 817 - 839 | |
| DOI | https://doi.org/10.1051/m2an/2022101 | |
| Published online | 30 March 2023 | |
Singular versus boundary arcs for aircraft trajectory optimization in climbing phase
1
Toulouse Univ., INP-ENSEEIHT-IRIT, UMR CNRS 5505, 2 rue Camichel, 31071 Toulouse, France
2
Thales Avionics SA, 105 av du General Eisenhower, B.P. 1147, 31047 Toulouse Cedex, France
* Corresponding author: olivier.cots@toulouse-inp.fr
Received:
21
March
2022
Accepted:
12
December
2022
In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant and we control the flight path angle of the aircraft. This optimization problem is modeled as a Mayer optimal control problem with a single-input affine dynamics in the control and with two pure state constraints, limiting the Calibrated AirSpeed (CAS) and the Mach speed. The candidates as minimizers are selected among a set of extremals given by the maximum principle. We first analyze the minimum time-to-climb problem with respect to the bounds of the state constraints, combining small time analysis, indirect multiple shooting and homotopy methods with monitoring. This investigation emphasizes two strategies: the common CAS/Mach procedure in aeronautics and the classical Bang-Singular-Bang policy in control theory. We then compare these two procedures for the cost index criterion.
Mathematics Subject Classification: 49K15 / 49M05 / 70Q05
Key words: Optimal control with state constraints / singular arcs / geometric control / homotopy method / aircraft trajectory optimization
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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