Geometric optimal control of elliptic Keplerian orbits

B. Bonnard; J.-B. Caillau; E. Trélat

doi:10.3934/dcdsb.2005.5.929

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2005, Volume 5, Issue 4: 929-956. Doi: 10.3934/dcdsb.2005.5.929

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Geometric optimal control of elliptic Keplerian orbits

1.
Institut de Mathématiques, Université de Bourgogne, 21078 Dijon
2.
ENSEEIHT-IRIT (UMR CNRS 5505), Institut National Polytechnique de Toulouse, 31071 Toulouse
3.
Laboratoire d'Analyse Numérique et EDP, Université de Paris-Sud, 91405 Orsay

Received: October 31, 2004

Revised: May 31, 2005

Published: October 2005

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Abstract

This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using the maximum principle. Second order sufficient conditions are also given. Finally, the time optimal trajectory to transfer the system from an initial low orbit with large eccentricity to a terminal geostationary orbit is obtained numerically.

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Mathematics Subject Classification: 49K15, 70Q05.

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