Second order optimality conditions in the smooth case and applications in optimal control

Bernard Bonnard; Jean-Baptiste Caillau; Emmanuel Trélat

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 2, page 207-236
  • ISSN: 1292-8119

Abstract

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The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate Times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. This algorithm involves both normal and abnormal cases.

How to cite

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Bonnard, Bernard, Caillau, Jean-Baptiste, and Trélat, Emmanuel. "Second order optimality conditions in the smooth case and applications in optimal control." ESAIM: Control, Optimisation and Calculus of Variations 13.2 (2007): 207-236. <http://eudml.org/doc/249984>.

@article{Bonnard2007,
abstract = { The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate Times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. This algorithm involves both normal and abnormal cases. },
author = {Bonnard, Bernard, Caillau, Jean-Baptiste, Trélat, Emmanuel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Conjugate point; second-order intrinsic derivative; Lagrangian singularity; Jacobi field; orbit transfer; attitude control; Conjugate points; Lagrangian singularity},
language = {eng},
month = {5},
number = {2},
pages = {207-236},
publisher = {EDP Sciences},
title = {Second order optimality conditions in the smooth case and applications in optimal control},
url = {http://eudml.org/doc/249984},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Bonnard, Bernard
AU - Caillau, Jean-Baptiste
AU - Trélat, Emmanuel
TI - Second order optimality conditions in the smooth case and applications in optimal control
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/5//
PB - EDP Sciences
VL - 13
IS - 2
SP - 207
EP - 236
AB - The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate Times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. This algorithm involves both normal and abnormal cases.
LA - eng
KW - Conjugate point; second-order intrinsic derivative; Lagrangian singularity; Jacobi field; orbit transfer; attitude control; Conjugate points; Lagrangian singularity
UR - http://eudml.org/doc/249984
ER -

References

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