Second order optimality conditions with applications

Bernard Bonnard (1) , Jean-Baptiste Caillau (1) , Emmanuel Trélat (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a point. An implementation of this algorithm, called cotcot, is available online and based on recent devel- opments in geometric optimal control. It is applied to analyze the averaged optimal transfer of a satellite between elliptic orbits.

Mots clés: Orbital transfer; time optimal control; Riemannian systems with drift; conjugate points

Domaines: Optimisation et contrôle [math.OC]

Bernard Bonnard, Jean-Baptiste Caillau, Emmanuel Trélat. Second order optimality conditions with applications. Discrete and Continuous Dynamical Systems - Series A, 2007, Dynamical Systems and Differential Equations, Proceedings of the 6th AIMS International Conference,, pp.145--154. ⟨hal-00105493⟩