On the role of abnormal minimizers in sub-Riemannian geometry

Bernard Bonnard (1) , Emmanuel Trélat (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at $0$ in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^\omega )$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.

Mots clés: optimal control; singular trajectories; sub-Riemannian geometry; abnormal minimizers; sphere and wave-front with small radii

Domaines: Optimisation et contrôle [math.OC]

Bernard Bonnard, Emmanuel Trélat. On the role of abnormal minimizers in sub-Riemannian geometry. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2001, 6 (10) 3, pp.405--491. ⟨hal-00086308⟩