A.A. Agrachev, Quadratic mappings in geometric control theory

Title: Quadratic mappings in geometric control theory
Authors: A.A. Agrachev
Journal title: Itogi Nauki i Tekhniki
Year: 1990
Issue: 6
Volume: 51
Pages: 2667-2734
Abstract:

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.