Control theory and optimization I
Subtitle: homogeneous spaces and the Riccati equation in the calculus of variations
By: by M.I. Zelikin ; translated by S.A. Vakhrameev
Series: Encyclopaedia of mathematical sciences -- 86
Publisher: Springer
Published: 2011
Place of publication: Berlin; London
Language: eng
Number of pages: 284
ISBN-13: 9783642086038
Subjects: Control theory; Commande, Théorie de la; Riccati, Équation de; Riccati equation; Optimisation mathématique; Mathematical optimization; Homogeneous spaces
Description: This book is devoted to geometric methods in the theory of differential equations with quadratic right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. Connections of the calculus of variations and the Riccati equation with the geometry of Lagrange-Grassmann manifolds and classical Cartan-Siegel homogeneity domains in a space of several complex variables are considered. In the study of the minimization problem for a multiple integral, a quadratic partial differential equation that is an analogue of the Riccati equation in the calculus of varatiations is studied. This book is based on lectures given by the author ower a period of several years in the Department of Mechanics and Mathematics of Moscow State University. The book is addressed to undergraduate and graduate students, scientific researchers and all specialists interested in the problems of geometry, the calculus of variations, and differential equations.
Notes: Originally published: 2000.

Translated from the Russian.