Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T21:36:13.829Z Has data issue: false hasContentIssue false
  • English
  • Français

Homotopy method for minimum consumption orbit transfer problem

Published online by Cambridge University Press:  22 March 2006

Joseph Gergaud  and
Thomas Haberkorn
Joseph Gergaud
Affiliation:
ENSEEIHT–IRIT, CNRS–UMR 5505, 2 rue Camichel, BP 7122, 31071 Toulouse Cedex 7, France; gergaud@enseeiht.fr
Thomas Haberkorn
Affiliation:
Mathematics Department, 2565 Mc Carthy Mall, Honolulu HI, 96822, USA; haberkor@math.hawaii.edu
Get access

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.

Keywords

Orbital transferoptimal control problemshooting methoddifferential homotopypredictor-corrector method.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 2 , April 2006 , pp. 294 - 310
Copyright
© EDP Sciences, SMAI, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

E.L. Allgower and K. Georg, Numerical Continuation Method. An Introduction. Springer-Verlag, Berlin (1990).
J.-P. Aubin and A. Cellina, Differential Inclusion. Springer-Verlag (1984).
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. http://www.enseeiht.fr/ caillau/papers/rt-01-3.html
Caillau, J.-B. and Noailles, J., Coplanar control of a satellite around the Earth. ESAIM: COCV 6 (2001) 239–258. CrossRef
L. Cesari, Optimization – Theory and Applications. Springer-Verlag (1983).
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).
J. Gergaud, T. Haberkorn and P. Martinon, Low thrust minimum-fuel orbital transfer: a homotopic approach. J. Guidance, Control, and Dynamics 27 (2004) 1046–1060.
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. http://www.enseeiht.fr/apo/mfmax/
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).
Oberle, H.J. and Taubert, K., Existence and multiple solutions of the minimum-fuel orbit transfer problem. J. Optim. Theory Appl. 95 (1997) 243–262. CrossRef
Watson, L.T., A globally convergent algorithm for computing fixed points of c 2 maps. Appl. Math. Comput. 5 (1979) 297–311. CrossRef
Watson, L.T., Sosonkina, M., Melville, R.C., Morgan, A.P. and Walker, H.F.. Algorithm 777: Hompack90: A suite of fortran 90 codes for globally convergent algorithms. ACM Trans. Math. Software 23 (1997) 514–549. CrossRef