Second order optimality conditions with applications

B. Bonnard; J.-B. Caillau; E. Trélat

doi:10.3934/proc.2007.2007.145

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2007, Volume 2007: 145-154. Doi: 10.3934/proc.2007.2007.145 open access

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Second order optimality conditions with applications

1.
Institut de Mathématiques, Université de Bourgogne, 21078 Dijon
2.
ENSEEIHT-IRIT (UMR CNRS 5505), Institut National Polytechnique de Toulouse, 31071 Toulouse
3.
Laboratoire MAPMO (UMR CNRS 6628), Université d'Orléans, 45067 Orléans

Received: July 31, 2006

Revised: February 28, 2007

Published: August 2007

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Abstract

An algorithm to compute the first conjugate point along a smooth extremal curve is presented. Under generic assumptions, the trajectory ceases to be locally optimal at such a point. An implementation of this algorithm, called cotcot, is available online and based on recent developments in geometric optimal control. It is applied to analyze the averaged optimal transfer of a satellite between elliptic orbits.

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Mathematics Subject Classification: 49K15, 70Q05.

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