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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  1. E.L. Allgower and K. Georg, Numerical Continuation Method. An Introduction. Springer-Verlag, Berlin (1990).  
  2. J.-P. Aubin and A. Cellina, Differential Inclusion. Springer-Verlag (1984).  
  3. J.-B. Caillau, J. Gergaud and J. Noailles, TfMin Short reference manual. Rapport de recherche RT/APO/01/3, ENSEEIHT-IRIT, UMR CNRS 5505, 2 rue Camichel, 31071 Toulouse, France, juillet 2001.  caillau/papers/rt-01-3.html  URIhttp://www.enseeiht.fr/
  4. J.-B. Caillau and J. Noailles, Coplanar control of a satellite around the Earth. ESAIM: COCV6 (2001) 239–258.  
  5. L. Cesari, Optimization – Theory and Applications. Springer-Verlag (1983).  
  6. J. Gergaud, Résolution numérique de problèmes de commande optimale à solution Bang-Bang par des méthodes homotopiques simpliciales. Ph.D. Thesis, ENSEEIHT, Institut National Polytechnique de Toulouse, France (janvier 1989).  
  7. J. Gergaud, T. Haberkorn and P. Martinon, Low thrust minimum-fuel orbital transfer: a homotopic approach. J. Guidance, Control, and Dynamics27 (2004) 1046–1060.  
  8. J. Gergaud, T. Haberkorn and J. Noailles, Mfmax(v0 and v1): Method explanation manual. Rapport de recherche RT/APO/04/1, ENSEEIHT-IRIT, UMR CNRS 5505, 2 rue Camichel, 31071 Toulouse, France, january 2004.  URIhttp://www.enseeiht.fr/apo/mfmax/
  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.  
  11. L.T. Watson, A globally convergent algorithm for computing fixed points of c2 maps. Appl. Math. Comput.5 (1979) 297–311.  
  12. L.T. Watson, M. Sosonkina, R.C. Melville, A.P. Morgan and H.F. Walker. Algorithm 777: Hompack90: A suite of fortran 90 codes for globally convergent algorithms. ACM Trans. Math. Software23 (1997) 514–549.  

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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