Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale

Bernard Bonnard; Emmanuel Trélat

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 179-222
  • ISSN: 1292-8119

Abstract

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The aim of this article is to make some geometric remarks and some preliminary calculations in order to construct the optimal atmospheric arc of a spatial shuttle (problem of reentry on Earth or Mars Sample Return project). The system describing the trajectories is in dimension 6, the control is the bank angle and the cost is the total thermal flux. Moreover there are state constraints (thermal flux, normal acceleration and dynamic pressure). Our study is mainly geometric and is founded on the evaluation of the accessibility set taking into account the state constraints. We make an analysis of the extremals of the Minimum Principle in the non-constrained case, and give a version of the Minimum Principle adapted to deal with the state constraints.

How to cite

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Bonnard, Bernard, and Trélat, Emmanuel. "Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 179-222. <http://eudml.org/doc/90618>.

@article{Bonnard2010,
abstract = { The aim of this article is to make some geometric remarks and some preliminary calculations in order to construct the optimal atmospheric arc of a spatial shuttle (problem of reentry on Earth or Mars Sample Return project). The system describing the trajectories is in dimension 6, the control is the bank angle and the cost is the total thermal flux. Moreover there are state constraints (thermal flux, normal acceleration and dynamic pressure). Our study is mainly geometric and is founded on the evaluation of the accessibility set taking into account the state constraints. We make an analysis of the extremals of the Minimum Principle in the non-constrained case, and give a version of the Minimum Principle adapted to deal with the state constraints. },
author = {Bonnard, Bernard, Trélat, Emmanuel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Contrôle optimal avec contraintes sur l'état; principes du minimum; mécanique céleste; arc atmosphérique.; optimal control with state constraints; minimum principle; celestial mechanics; atmospheric arc},
language = {eng},
month = {3},
pages = {179-222},
publisher = {EDP Sciences},
title = {Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale},
url = {http://eudml.org/doc/90618},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Bonnard, Bernard
AU - Trélat, Emmanuel
TI - Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 179
EP - 222
AB - The aim of this article is to make some geometric remarks and some preliminary calculations in order to construct the optimal atmospheric arc of a spatial shuttle (problem of reentry on Earth or Mars Sample Return project). The system describing the trajectories is in dimension 6, the control is the bank angle and the cost is the total thermal flux. Moreover there are state constraints (thermal flux, normal acceleration and dynamic pressure). Our study is mainly geometric and is founded on the evaluation of the accessibility set taking into account the state constraints. We make an analysis of the extremals of the Minimum Principle in the non-constrained case, and give a version of the Minimum Principle adapted to deal with the state constraints.
LA - eng
KW - Contrôle optimal avec contraintes sur l'état; principes du minimum; mécanique céleste; arc atmosphérique.; optimal control with state constraints; minimum principle; celestial mechanics; atmospheric arc
UR - http://eudml.org/doc/90618
ER -

References

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