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Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines

Bensalem, Naceurdine — 2008

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 49J15, 49J30, 53B50. In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.

Some geometrical properties of infinite-dimensional bilinear controlled systems

Naceurdine Bensalem;  Fernand Pelletier — 1999

Banach Center Publications

The study of controlled infinite-dimensional systems gives rise to many papers (see for instance [GXL], [GXB], [X]) but it is also motivated by various mathematical problems: partial differential equations ([BP]), sub-Riemannian geometry on infinite-dimensional manifolds ([Gr]), deformations in loop-spaces ([AP], [PS]). The first difference between finite and infinite-dimensional cases is that solutions in general do not exist (even locally) for every given control function. The aim of this paper...

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