# 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

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topBonnard, 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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## Citations in EuDML Documents

top- Bernard Bonnard, Jean-Baptiste Caillau, Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
- Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny, The smooth continuation method in optimal control with an application to quantum systems
- Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny, The smooth continuation method in optimal control with an application to quantum systems

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