École Nationale Supérieure de
Techniques Avancées

Abstract

The two key questions are: (a) the uniqueness of a cost for a given optimal synthesis; (b) the reconstruction of the cost from the synthesis. For general classes of costs, the problem seems very difficult even with a trivial dynamics. Our goal is to address these two questions for problems having a quadratic cost and a dynamics that can be either trivial (Riemannian geometry) or non-holonomic (sub-Riemannian geometry) or control-affine.