Conjugate and cut loci of a two-sphere of revolution with application to optimal control

Bernard Bonnard (1) , Jean-Baptiste Caillau (2) , Robert Sinclair (3) , Minoru Tanaka (4)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 IRIT-APO - Algorithmes Parallèles et Optimisation
3 Okinawa Institute of Science and Technology
4 Tokai University

The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and give global optimal results in orbital transfer and for Redfield equations in quantum control.

Mots clés: conjugate and cut loci; 2-spheres of revolution; optimal control; space and quantum mechanics

Domaines: Optimisation et contrôle [math.OC]

Bernard Bonnard, Jean-Baptiste Caillau, Robert Sinclair, Minoru Tanaka. Conjugate and cut loci of a two-sphere of revolution with application to optimal control. 2008. ⟨hal-00212075v2⟩