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Discrete and differential homotopy in circular restricted three-body control

Pages: 229 - 239, Issue Special, September 2011

 Abstract        Full Text (2281.4K)              

Jean-Baptiste Caillau - Math. Institute, Bourgogne Univ. & CRNS, 9 avenue Savary, F-21078 Dijon, France (email)
Bilel Daoud - Math. Institute, Bourgogne Univ. & CNRS, 9 avenue Savary, F-21078 Dijon, France (email)
Joseph Gergaud - Math. Institute, Bourgogne Univ. & CRNS, 9 avenue Savary, F-21078 Dijon, France (email)

Abstract: The planar circular restricted three-body problem is considered. The control enters linearly in the equation of motion to model the thrust of the third body. The minimum time optimal control problem has two scalar parameters: The ratio of the primaries masses which embeds the two-body problem into the three-body one, and the upper bound on the control norm. Regular extremals of the maximum principle are computed by shooting thanks to continuations with respect to both parameters. Discrete and di erential homotopy are compared in connection with second order sucient conditions in optimal control. Homotopy with respect to control bound gives evidence of various topological structures of extremals.

Keywords:  Time optimal control, circular restricted three-body problem, discrete and di erential homotopy, conjugate points
Mathematics Subject Classification:  Primary: 49K15, 70Q05

Received: August 2010;      Revised: May 2011;      Published: October 2011.