Second order optimality conditions in optimal control with applications
Résumé
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point. An implementation of this algorithm, called \texttt{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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