Search results for "Continuous function"

showing 4 items of 24 documents

3D Geosynchronous Transfer of a Satellite: Continuation on the Thrust

2003

The minimum-time transfer of a satellite from a low and eccentric initial orbit toward a high geostationary orbit is considered. This study is preliminary to the analysis of similar transfer cases with more complicated performance indexes (maximization of payload, for instance). The orbital inclination of the spacecraft is taken into account (3D model), and the thrust available is assumed to be very small (e.g. 0.3 Newton for an initial mass of 1500 kg). For this reason, many revolutions are required to achieve the transfer and the problem becomes very oscillatory. In order to solve it numerically, an optimal control model is investigated and a homotopic procedure is introduced, namely cont…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyControl and OptimizationContinuous functionApplied MathematicsGeosynchronous orbit[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Thrust02 engineering and technologyManagement Science and Operations ResearchOptimal control01 natural sciencesOrbital inclination020901 industrial engineering & automationShooting methodControl theory0103 physical sciencesOrbit (dynamics)Geostationary orbit[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]010303 astronomy & astrophysicsComputingMilieux_MISCELLANEOUSMathematics
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Existence and classification of critical points for nondifferentiable functions

2004

A general min-max principle established by Ghoussoub is extended to the case of functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. Some topological properties of the min-max-generated critical points in such a framework are then pointed out.

locally Lipschitz continus functionlower semicontinuous functionApplied Mathematicsconvexcritical pointAnalysipropercritical point; locally Lipschitz continus function; convex proper lower semicontinuous function49J3558E05Analysis47J30
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Representing compact sets of compact operators and of compact range vector measures

1987

symbols.namesakeApproximation propertyNuclear operatorGeneral MathematicsHilbert spacesymbolsFinite-rank operatorCompact operatorTopologyInvariant subspace problemContinuous functions on a compact Hausdorff spaceCompact operator on Hilbert spaceMathematicsArchiv der Mathematik
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Relaxation of a weakly discontinuous functional depending on one control function

2008

The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.

weakly discontinuous functionalMathematical analysisType (model theory)Optimal controlControl functionSet (abstract data type)elliptic systemoptimal controlrelaxationControl theoryModeling and SimulationQA1-939Relaxation (approximation)AnalysisMathematicsMathematicsMathematical Modelling and Analysis
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