Coplanar control of a satellite around the Earth
Jean-Baptiste Caillau; Joseph Noailles
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 6, page 239-258
- ISSN: 1292-8119
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topCaillau, Jean-Baptiste, and Noailles, Joseph. "Coplanar control of a satellite around the Earth." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 239-258. <http://eudml.org/doc/197349>.
@article{Caillau2010,
abstract = {
We investigate the minimum time transfer of a
satellite around the Earth. Using an optimal control model, we study
the controllability of the system and propose a geometrical analysis
of the optimal command structure. Furthermore, in order to solve the
problem numerically, a new parametric technique is introduced for
which convergence properties are established.
},
author = {Caillau, Jean-Baptiste, Noailles, Joseph},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Celestial mechanics; minimum time problems; geometric control; parametric optimal control.; minimum time transfer; parametric optimal control; controllability; convergence},
language = {eng},
month = {3},
pages = {239-258},
publisher = {EDP Sciences},
title = {Coplanar control of a satellite around the Earth},
url = {http://eudml.org/doc/197349},
volume = {6},
year = {2010},
}
TY - JOUR
AU - Caillau, Jean-Baptiste
AU - Noailles, Joseph
TI - Coplanar control of a satellite around the Earth
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 239
EP - 258
AB -
We investigate the minimum time transfer of a
satellite around the Earth. Using an optimal control model, we study
the controllability of the system and propose a geometrical analysis
of the optimal command structure. Furthermore, in order to solve the
problem numerically, a new parametric technique is introduced for
which convergence properties are established.
LA - eng
KW - Celestial mechanics; minimum time problems; geometric control; parametric optimal control.; minimum time transfer; parametric optimal control; controllability; convergence
UR - http://eudml.org/doc/197349
ER -
References
top- B. Bonnard and J. de Morant, Towards a geometric theory in the time minimal control of chemical batch reactors. SIAM J. Control Optim.33 (1995) 1279-1311.
- B. Bonnard and G. Launay, Time minimal control of batch reactors. ESAIM: COCV3 (1998) 407-467.
- J.B. Caillau, Contribution à l'étude du contren temps minimal des transferts orbitaux. Ph.D. Thesis, ENSEEIHT, Institut National Polytechnique de Toulouse, France (2000).
- J.B. Caillau and J. Noailles, Continuous optimal control sensitivity analysis with AD, in Proc. of the 3rd International Conference on Automatic Differentiation. INRIA Nice, France (2000).
- J.B. Caillau and J. Noailles, Sensitivity analysis for time optimal orbit transfer. Optimization49 (2001) 327-350.
- L. Cesari, Optimization Theory and Applications. Springer-Verlag (1983).
- C. Ferrier and R. Epenoy, Optimal control for engines with electro-ionic propulsion under constraint of eclipse. Acta Astronautica (to appear).
- M. Fliess, Variations sur la notion de contré, in Quelques aspects de la théorie du contr. Journée Annuelle de la Société Mathématique de France (2000).
- S. Geffroy, R. Epenoy and J. Noailles, Averaging techniques in optimal control for orbital low-thrust transfers and rendez-vous computation, in 11th International Astrodynamics Symposium. Gifu, Japan (1996) 166-171.
- M. Godbillon, Géométrie différentielle et mécanique analytique. Hermann, Paris (1985).
- V. Jurdjevic, Geometric control theory. Cambridge University Press (1997).
- K. Malanowski, Sufficient optimality conditions for optimal control subject to state constraints. SIAM J. Control Optim.35 (1997) 205-227.
- K. Malanowski and H. Maurer, Sensitivity analysis for parametric optimal control problems with control-state constraints. Comp. Optim. Appl.5 (1996) 253-283.
- J. Noailles and J. Gergaud, A new method for the time optimal control problem and its application to low thrust orbital transfer. Workshop on low thrust transfers, Toulouse, France, French Space Agency, CNES (2000).
- J. Noailles and T.C. Le, Contren temps minimal et transfert orbital à faible poussée. Équations aux dérivées partielles et applications, articles in honour of J.L. Lions for his 70th birthday. Gauthier-Villars (1998) 705-724.
- H.J. Sussmann, Geometry and Optimal Control, in Mathematical Control Theory, Dedicated to Roger W. Brockett on his 60th birthday, edited by J. Baillieul and J.C. Willems. Springer-Verlag (1998).
- H.J. Sussmann, Résultats récents sur les courbes optimales, in Quelques aspects de la théorie du contr. Journée Annuelle de la Société Mathématique de France (2000).
- O. Zarrouati, Trajectoires spatiales. CNES-Cepadues, Toulouse, France (1987).
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