6533b830fe1ef96bd129668b
RESEARCH PRODUCT
Discrete and differential homotopy in circular restricted three-body control
Joseph GergaudJean-baptiste CaillauBilel Daoudsubject
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Homotopy lifting propertyHomotopy010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal control01 natural sciencesUpper and lower boundsRegular homotopyn-connectedMaximum principle0103 physical sciences[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematics010303 astronomy & astrophysicsHomotopy analysis methodComputingMilieux_MISCELLANEOUSMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-05-01 |