# Seminar of Ludovic Sacchelli, University of Toulon

Here is the title and summary of Ludovic Sacchelli’s seminar:

Title: Sub-Riemannian Extremals for Contact Distributions

Abstract: The contact manifolds are odd-dimensional state spaces whose distribution consisting of hyperplanes is generating by Lie hooks at any point. In these spaces, we are interested in the optimal control of systems with linear dynamics in control and non-linear in state, with penalization of the norm L2 of the control, measured according to a so-called sub-Riemannian metric.
Following the work of Agrachev, Gauthier and their collaborators having carried out the in-depth study of the case of dimension 3 since the mid-90s, we seek to characterize the family of small extremals emanating from a point. In particular, by perturbative methods, we are interested in studying the geometry of the singular place, the set of points of loss of local optimality of the extremals. ”

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