American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 145-154. doi: 10.3934/proc.2007.2007.145

Second order optimality conditions with applications

B. Bonnard 1, , J.-B. Caillau 2, and  E. Trélat 3,

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, France

Received  August 2006 Revised  March 2007 Published  September 2007

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.
Keywords: time optimal control, conjugate points., Riemannian systems with drift, Orbital transfer.
Mathematics Subject Classification: 49K15, 70Q0.
Citation: B. Bonnard, J.-B. Caillau, E. Trélat. Second order optimality conditions with applications. Conference Publications, 2007, 2007 (Special) : 145-154. doi: 10.3934/proc.2007.2007.145
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