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

Abstract

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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.

How to cite

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Gergaud, 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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  9. T. Haberkorn, Transfert orbital à poussée faible avec minimisation de la consommation: résolution par homotopie différentielle. Ph.D. Thesis, ENSEEIHT, Institut National Polytechnique de Toulouse, France (octobre 2004).  
  10. H.J. Oberle and K. Taubert, Existence and multiple solutions of the minimum-fuel orbit transfer problem. J. Optim. Theory Appl.95 (1997) 243–262.  
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Citations in EuDML Documents

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  1. Bernard Bonnard, Jean-Baptiste Caillau, Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
  2. Joseph Frédéric Bonnans, Audrey Hermant, Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
  3. Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny, The smooth continuation method in optimal control with an application to quantum systems
  4. Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny, The smooth continuation method in optimal control with an application to quantum systems

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