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Conjugate and cut loci of a two-sphere of revolution with application to optimal control |
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| Authors: | Bernard Bonnard Jean-Baptiste Caillau Robert Sinclair Minoru Tanaka |
| Affiliation: | aInstitut de mathématiques de Bourgogne (UMR CNRS 5584), 9, avenue Savary, F-21078 Dijon, France;bENSEEIHT-IRIT (UMR CNRS 5505), 2, rue Camichel, F-31071 Toulouse, France;cMathematical Biology Unit, Okinawa Institute of Science and Technology, Okinawa Industrial Technology Center Annex, 12-2 Suzaki, Uruma, Okinawa 904-2234, Japan;dDepartment of Mathematics, Tokai University, Hiratsuka City, Kanagawa Pref., 259-1292, Japan |
| Abstract: | 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 gives global optimal results in orbital transfer and for Lindblad equations in quantum control. |
| Keywords: | Conjugate and cut loci 2-spheres of revolution Optimal control Space and quantum mechanics |
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