The article is dedicated to local investigation of mappings of type "input-state" of smooth controlled systems. The homological theory of quadratic mappings and the geometry of the Lagrange Grassmannian are used for the study of mappings of type "input-state" including for the obtaining of the necessary and sufficient conditions for local optimality.
Title: Quadratic mappings in geometric control theory
Authors: A.A. Agrachev
Journal title: Itogi Nauki i Tekhniki