0000000000319140

AUTHOR

Ludovic Faubourg

showing 3 related works from this author

Conjugate times for smooth singular trajectories and bang-bang extremals

2003

Abstract In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the intrinsic second order derivative or the exponential mapping. An algorithm is given which was implemented in the SR-case to compute the caustic [1] or in recent applied problems [5],[9]. We investigate briefly the problem of using this algorithm in the bang-bang case by smoothing the corners of extremals

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyPhysics::General Physics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technology01 natural sciences020901 industrial engineering & automationExponential mappingCaustic (optics)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsBang bangBang–bang controlSmoothingMathematicsConjugateSecond derivative
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Classification of local optimal syntheses for time minimal control problems with state constraints

2003

This paper describes the analysis under generic assumptions of the small \textit{time minimal syntheses} for single input affine control systems in dimension $3$, submitted to \textit{state constraints}. We use geometric methods to evaluate \textit{the small time reachable set} and necessary optimality conditions. Our work is motivated by the \textit{optimal control of the atmospheric arc for the re-entry of a space shuttle}, where the vehicle is subject to constraints on the thermal flux and on the normal acceleration.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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Optimal control of the atmospheric arc of a space shuttle and numerical simulations with multiple-shooting method

2005

This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the thermal flux, the normal acceleration and the dynamic pressure. Our analysis is based on the evaluation of the reachable set using the maximum principle and direct computations with the boundary conditions according to the CNES research project\footnote{The project is partially supported by the Centre National d'Etude Spatiales.}. The optimal solution is approximated by a concatenat…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnology49K15 70M2049M15Boundary (topology)Space Shuttlemultiple-shooting method02 engineering and technology01 natural sciencesAcceleration020901 industrial engineering & automationShooting methodMaximum principleControl theoryBoundary value problemcontrol of the atmospheric arc0101 mathematicsMathematicsmultiple-shooting method.Applied Mathematics010102 general mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal controlHeat fluxModeling and SimulationOptimal control with state constraints[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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