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Quadratic mappings in geometric control theory. (English) Zbl 1267.93035
J. Sov. Math. 51, No. 6, 2667-2734 (1990); translation from Itogi Nauki Tekh., Ser. Probl. Geom. 20, 111–206 (1988).
Summary: The article is dedicated to local investigation of mappings of type “entry-exit” of smooth controlled systems. The homological theory of quadratic mappings and the geometry of the Lagrange Grassmannian are used for the study of sets of the level and the form of mappings of type “entry-exit,” including for the obtaining of the necessary and sufficient conditions for local optimality.

MSC:
93B27 Geometric methods
49K15 Optimality conditions for problems involving ordinary differential equations
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