Coplanar control of a satellite around the earth
ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 239-258.

On s'intéresse au transfert en temps minimal d'un satellite autour de la Terre. Sur la base d'une modélisation contrôle optimal, on étudie la controlabilité du système et on propose une analyse de la structure de la commande optimale. En outre, afin de procéder à la résolution numérique du problème, une nouvelle méthode paramétrique dont on établit des propriétés de convergence est définie.

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.

Classification : 70Q05, 49M30, 93B29
Mots-clés : celestial mechanics, minimum time problems, geometric control, parametric optimal control 
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     title = {Coplanar control of a satellite around the earth},
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Caillau, Jean-Baptiste; Noailles, Joseph. Coplanar control of a satellite around the earth. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 239-258. http://archive.numdam.org/item/COCV_2001__6__239_0/

[1] 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. | Zbl

[2] B. Bonnard and G. Launay, Time minimal control of batch reactors. ESAIM: COCV 3 (1998) 407-467. | Numdam | Zbl

[3] J.B. Caillau, Contribution à l'étude du contrôle en temps minimal des transferts orbitaux. Ph.D. Thesis, ENSEEIHT, Institut National Polytechnique de Toulouse, France (2000).

[4] 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).

[5] J.B. Caillau and J. Noailles, Sensitivity analysis for time optimal orbit transfer. Optimization 49 (2001) 327-350. | Zbl

[6] L. Cesari, Optimization Theory and Applications. Springer-Verlag (1983). | MR | Zbl

[7] C. Ferrier and R. Epenoy, Optimal control for engines with electro-ionic propulsion under constraint of eclipse. Acta Astronautica (to appear).

[8] M. Fliess, Variations sur la notion de contrôlabilité, in Quelques aspects de la théorie du contrôle. Journée Annuelle de la Société Mathématique de France (2000). | MR | Zbl

[9] S. Geffroy, R. Epenoy and J. Noailles, Averaging techniques in optimal control for orbital low-thrust transfers and rendez-vous computation1996) 166-171.

[10] M. Godbillon, Géométrie différentielle et mécanique analytique. Hermann, Paris (1985). | Zbl

[11] V. Jurdjevic, Geometric control theory. Cambridge University Press (1997). | MR | Zbl

[12] K. Malanowski, Sufficient optimality conditions for optimal control subject to state constraints. SIAM J. Control Optim. 35 (1997) 205-227. | Zbl

[13] K. Malanowski and H. Maurer, Sensitivity analysis for parametric optimal control problems with control-state constraints. Comp. Optim. Appl. 5 (1996) 253-283. | Zbl

[14] 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).

[15] J. Noailles and T.C. Le, Contrôle en temps minimal et transfert orbital à faible poussée1998) 705-724. | Zbl

[16] H.J. Sussmann, Geometry and Optimal Control1998). | MR | Zbl

[17] H.J. Sussmann, Résultats récents sur les courbes optimales, in Quelques aspects de la théorie du contrôle. Journée Annuelle de la Société Mathématique de France (2000). | MR | Zbl

[18] O. Zarrouati, Trajectoires spatiales. CNES-Cepadues, Toulouse, France (1987).