0000000000002804

AUTHOR

Bilel Daoud

showing 4 related works from this author

Minimum fuel control of the planar circular restricted three-body problem

2012

The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point bound…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Lagrangian point02 engineering and technology01 natural sciences0203 mechanical engineeringControl theory0103 physical sciencesApplied mathematicsBoundary value problemCircular orbit010303 astronomy & astrophysicsComputingMilieux_MISCELLANEOUSMathematical PhysicsMathematics020301 aerospace & aeronauticsApplied MathematicsConjugate points[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Astronomy and AstrophysicsOptimal controlThree-body problemControllabilityComputational MathematicsSpace and Planetary ScienceModeling and Simulation[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Hamiltonian (control theory)Celestial Mechanics and Dynamical Astronomy
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Minimum Time Control of the Restricted Three-Body Problem

2012

The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Surface (mathematics)0209 industrial biotechnologyControl and OptimizationApplied MathematicsHomotopy010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyThree-body problemOptimal controlSubmanifold01 natural sciencesControllability020901 industrial engineering & automationSimple (abstract algebra)Gravitational singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsMathematicsSIAM Journal on Control and Optimization
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Discrete and differential homotopy in circular restricted three-body control

2010

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 extr…

[ 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_MISCELLANEOUSMathematics
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On some Riemannian aspects of two and three-body controlled problems

2009

The flow of the Kepler problem (motion of two mutually attracting bodies) is known to be geodesic after the work of Moser [20], extended by Belbruno and Osipov [2, 21]: Trajectories are reparameterizations of minimum length curves for some Riemannian metric. This is not true anymore in the case of the three-body problem, and there are topological obstructions as observed by McCord et al. [19]. The controlled formulations of these two problems are considered so as to model the motion of a spacecraft within the influence of one or two planets. The averaged flow of the (energy minimum) controlled Kepler problem with two controls is shown to remain geodesic. The same holds true in the case of o…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Work (thermodynamics)Geodesic010102 general mathematicsMathematical analysisMotion (geometry)[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal control01 natural sciencesOptimal controlsymbols.namesakeFlow (mathematics)Kepler problemCut and conjugate loci0103 physical sciencesMetric (mathematics)symbolsGeodesic flowTwo and three-body problems49K15 53C20 70Q05Gravitational singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematics010303 astronomy & astrophysicsMathematics
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