---
_id: '59504'
abstract:
- lang: eng
  text: '<jats:p>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.</jats:p>'
author:
- first_name: Olivier
  full_name: Cots, Olivier
  last_name: Cots
- first_name: Joseph
  full_name: Gergaud, Joseph
  last_name: Gergaud
- first_name: Damien
  full_name: Goubinat, Damien
  last_name: Goubinat
- first_name: Boris
  full_name: Wembe, Boris
  last_name: Wembe
citation:
  ama: 'Cots O, Gergaud J, Goubinat D, Wembe B. Singular <i>versus</i> boundary arcs
    for aircraft trajectory optimization in climbing phase. <i>ESAIM: Mathematical
    Modelling and Numerical Analysis</i>. 2022;57(2):817-839. doi:<a href="https://doi.org/10.1051/m2an/2022101">10.1051/m2an/2022101</a>'
  apa: 'Cots, O., Gergaud, J., Goubinat, D., &#38; Wembe, B. (2022). Singular <i>versus</i>
    boundary arcs for aircraft trajectory optimization in climbing phase. <i>ESAIM:
    Mathematical Modelling and Numerical Analysis</i>, <i>57</i>(2), 817–839. <a href="https://doi.org/10.1051/m2an/2022101">https://doi.org/10.1051/m2an/2022101</a>'
  bibtex: '@article{Cots_Gergaud_Goubinat_Wembe_2022, title={Singular <i>versus</i>
    boundary arcs for aircraft trajectory optimization in climbing phase}, volume={57},
    DOI={<a href="https://doi.org/10.1051/m2an/2022101">10.1051/m2an/2022101</a>},
    number={2}, journal={ESAIM: Mathematical Modelling and Numerical Analysis}, publisher={EDP
    Sciences}, author={Cots, Olivier and Gergaud, Joseph and Goubinat, Damien and
    Wembe, Boris}, year={2022}, pages={817–839} }'
  chicago: 'Cots, Olivier, Joseph Gergaud, Damien Goubinat, and Boris Wembe. “Singular
    <i>versus</i> Boundary Arcs for Aircraft Trajectory Optimization in Climbing Phase.”
    <i>ESAIM: Mathematical Modelling and Numerical Analysis</i> 57, no. 2 (2022):
    817–39. <a href="https://doi.org/10.1051/m2an/2022101">https://doi.org/10.1051/m2an/2022101</a>.'
  ieee: 'O. Cots, J. Gergaud, D. Goubinat, and B. Wembe, “Singular <i>versus</i> boundary
    arcs for aircraft trajectory optimization in climbing phase,” <i>ESAIM: Mathematical
    Modelling and Numerical Analysis</i>, vol. 57, no. 2, pp. 817–839, 2022, doi:
    <a href="https://doi.org/10.1051/m2an/2022101">10.1051/m2an/2022101</a>.'
  mla: 'Cots, Olivier, et al. “Singular <i>versus</i> Boundary Arcs for Aircraft Trajectory
    Optimization in Climbing Phase.” <i>ESAIM: Mathematical Modelling and Numerical
    Analysis</i>, vol. 57, no. 2, EDP Sciences, 2022, pp. 817–39, doi:<a href="https://doi.org/10.1051/m2an/2022101">10.1051/m2an/2022101</a>.'
  short: 'O. Cots, J. Gergaud, D. Goubinat, B. Wembe, ESAIM: Mathematical Modelling
    and Numerical Analysis 57 (2022) 817–839.'
date_created: 2025-04-10T14:34:18Z
date_updated: 2025-04-10T14:39:50Z
doi: 10.1051/m2an/2022101
intvolume: '        57'
issue: '2'
language:
- iso: eng
page: 817-839
publication: 'ESAIM: Mathematical Modelling and Numerical Analysis'
publication_identifier:
  issn:
  - 2822-7840
  - 2804-7214
publication_status: published
publisher: EDP Sciences
status: public
title: Singular <i>versus</i> boundary arcs for aircraft trajectory optimization in
  climbing phase
type: journal_article
user_id: '95394'
volume: 57
year: '2022'
...