Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T07:56:14.616Z Has data issue: false hasContentIssue false
  • English
  • Français

Coplanar control of a satellite around the Earth

Published online by Cambridge University Press:  15 August 2002

Jean-Baptiste Caillau  and
Joseph Noailles
Jean-Baptiste Caillau
Affiliation:
ENSEEIHT–IRIT, UMR 5505 du CNRS, 2 rue Camichel, 31071 Toulouse, France
Joseph Noailles
Affiliation:
ENSEEIHT–IRIT, UMR 5505 du CNRS, 2 rue Camichel, 31071 Toulouse, France
Get access

Abstract

We investigate the minimum time transfer of asatellite around the Earth. Using an optimal control model, we studythe controllability of the system and propose a geometrical analysisof the optimal command structure. Furthermore, in order to solve theproblem numerically, a new parametric technique is introduced forwhich convergence properties are established.

Keywords

Celestial mechanicsminimum time problemsgeometric controlparametric optimal control.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 239 - 258
Copyright
© EDP Sciences, SMAI, 2001

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

Bonnard, B. and de Morant, J., Towards a geometric theory in the time minimal control of chemical batch reactors. SIAM J. Control Optim. 33 (1995) 1279-1311. CrossRef
Bonnard, B. and Launay, G., Time minimal control of batch reactors. ESAIM: COCV 3 (1998) 407-467. CrossRef
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).
Caillau, J.B. and Noailles, J., Sensitivity analysis for time optimal orbit transfer. Optimization 49 (2001) 327-350. CrossRef
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 11 th 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).
Malanowski, K., Sufficient optimality conditions for optimal control subject to state constraints. SIAM J. Control Optim. 35 (1997) 205-227. CrossRef
Malanowski, K. and Maurer, H., Sensitivity analysis for parametric optimal control problems with control-state constraints. Comp. Optim. Appl. 5 (1996) 253-283. CrossRef
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).