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2011, Volume 2011: 229-239. Doi: 10.3934/proc.2011.2011.229 open access
This issue Previous Article Symmetry breaking in problems involving semilinear equations Next Article Decay rate at infinity of the positive solutions of a generalized class of $T$homas-Fermi equations

Discrete and differential homotopy in circular restricted three-body control

  • 1.

    Math. Institute, Bourgogne Univ. & CRNS, 9 avenue Savary, F-21078 Dijon

  • 2.

    Math. Institute, Bourgogne Univ. & CNRS, 9 avenue Savary, F-21078 Dijon

Received:  July 31, 2010
Revised:  April 30, 2011
Published:  August 2017
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 49K15, 70Q05.

    Citation:
    shu

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