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Local study of sub-Finslerian control systems

Abstract : In this thesis I study the local geometry of Finslerian and sub-Finslerian structures associated to the maximum norm in dimension 2 and 3 : short generalized geodesics, cut locus, generalized conjugate locus, switching locus, small spheres.To define such a structure in the neighborhood of a point p of mathbb{R} n, we fix a familly of vector fields (F 1,dots,F k) and consider the norm defined on the distribution Delta=mbox {vect}{F 1,dots,F k} by |G|=inf{max{|u i|} ; | ; G=sum i u i F i} .In dimension 2, for k=2, if F 1 and F 2 are not proportionnal at p then we obtain a Finslerian structure. If not, the structure is sub-Finslerian on a distribution with non constant rank. We describe the geometric objects for the set of all generic couples (F 1, F 2).In dimension 3, we studied the local geometry for contact distributions.
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Submitted on : Friday, January 12, 2018 - 2:46:27 PM
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  • HAL Id : tel-01681328, version 2



Entisar Abdul-Latif Ali. Local study of sub-Finslerian control systems. Optimization and Control [math.OC]. Université Grenoble Alpes, 2017. English. ⟨NNT : 2017GREAM005⟩. ⟨tel-01681328v2⟩



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