# Homotopy method for minimum consumption orbit transfer problem

Joseph Gergaud; Thomas Haberkorn

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 2, page 294-310
- ISSN: 1292-8119

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topGergaud, Joseph, and Haberkorn, Thomas. "Homotopy method for minimum consumption orbit transfer problem." ESAIM: Control, Optimisation and Calculus of Variations 12.2 (2006): 294-310. <http://eudml.org/doc/249666>.

@article{Gergaud2006,

abstract = {
The numerical resolution of the low thrust orbital transfer problem around the Earth with the maximization of the final mass or minimization of the consumption is investigated. This problem is difficult to solve by shooting method because the optimal control is discontinuous and a homotopic method is proposed to deal with these difficulties for which convergence properties are established. For a thrust of 0.1 Newton and a final time 50% greater than the minimum one, we obtain 1786 switching times.
},

author = {Gergaud, Joseph, Haberkorn, Thomas},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Orbital transfer; optimal control problem; shooting method; differential homotopy; predictor-corrector method.; predictor-corrector method},

language = {eng},

month = {3},

number = {2},

pages = {294-310},

publisher = {EDP Sciences},

title = {Homotopy method for minimum consumption orbit transfer problem},

url = {http://eudml.org/doc/249666},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Gergaud, Joseph

AU - Haberkorn, Thomas

TI - Homotopy method for minimum consumption orbit transfer problem

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/3//

PB - EDP Sciences

VL - 12

IS - 2

SP - 294

EP - 310

AB -
The numerical resolution of the low thrust orbital transfer problem around the Earth with the maximization of the final mass or minimization of the consumption is investigated. This problem is difficult to solve by shooting method because the optimal control is discontinuous and a homotopic method is proposed to deal with these difficulties for which convergence properties are established. For a thrust of 0.1 Newton and a final time 50% greater than the minimum one, we obtain 1786 switching times.

LA - eng

KW - Orbital transfer; optimal control problem; shooting method; differential homotopy; predictor-corrector method.; predictor-corrector method

UR - http://eudml.org/doc/249666

ER -

## References

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- 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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