Regular syntheses and solutions to discontinuous ODEs

Alessia Marigo; Benedetto Piccoli

Displaying similar documents to “Regular syntheses and solutions to discontinuous ODEs”

Asymptotics of accessibility sets along an abnormal trajectory

Emmanuel Trélat (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-riemannian system of rank 2. As a consequence we obtain in sub-riemannian geometry a new splitting-up of the sphere near an abnormal minimizer $γ$ into two sectors, bordered by the first Pontryagin’s cone along $γ$ , called the $L^{\infty}$ -sector and the $L^{2}$ -sector....