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Second order optimality conditions in the smooth case and applications in optimal control

Bernard Bonnard, Jean-Baptiste Caillau, Emmanuel Trélat (2007)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions...

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