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In this paper we investigate analytic affine control systems q̇ = X + uY, u ∈ [a,b] , where X,Y is an orthonormal frame for a generalized Martinet sub-Lorentzian structure of order k of Hamiltonian type. We construct normal forms for such systems and, among other things, we study the connection between the presence of the singular trajectory starting at q0 on the boundary of the reachable set from q0 with the minimal number of analytic functions needed for describing the reachable set from q0.
Dans cet article nous prouvons un nouveau résultat d'existence pour une
classe de problèmes d'optimisation de forme assez générale. Les ouverts
que nous considérons possèdent une contrainte de nature géométrique
sur la normale intérieure. Ce travail est motivé par la formulation
variationnelle d'un problème à frontière libre dont la solution possède
cette propriété géométrique.
The aim of this paper is to summarize basic facts about -stable at a point vector functions and existing results for certain vector constrained programming problem with -stable data.
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