Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equatio in the Calculus of Variations - Couverture rigide

Livre 20 sur 47: Encyclopaedia of Mathematical Sciences

Zelikin, M.I.

 
9783540667414: Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equatio in the Calculus of Variations
Couverture rigide
ISBN 10 : 3540667415 ISBN 13 : 9783540667414
Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1999

Synopsis

This book is devoted to the development of geometrie methods for studying and revealing geometrie aspects of the theory of differential equations with quadratie right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. The book contains the following three parts, to each of which aseparate book could be devoted: 1. the classieal calculus of variations and the geometrie theory of the Riccati equation (Chaps. 1-5), 2. complex Riccati equations as flows on Cartan-Siegel homogeneity da- mains (Chap. 6), and 3. the minimization problem for multiple integrals and Riccati partial dif- ferential equations (Chaps. 7 and 8). Chapters 1-4 are mainly auxiliary. To make the presentation complete and self-contained, I here review the standard facts (needed in what folIows) from the calculus of variations, Lie groups and algebras, and the geometry of Grass- mann and Lagrange-Grassmann manifolds. When choosing these facts, I pre- fer to present not the most general but the simplest assertions. Moreover, I try to organize the presentation so that it is not obscured by formal and technical details and, at the same time, is sufficiently precise. Other chapters contain my results concerning the matrix double ratio, com- plex Riccati equations, and also the Riccati partial differential equation, whieh the minimization problem for a multiple integral. arises in The book is based on a course of lectures given in the Department of Me- and Mathematics of Moscow State University during several years.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Date d'édition
1999
Langue
anglais
ISBN 10 
3540667415
ISBN 13 
9783540667414
Reliure
Relié
Nombre de pages
296
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9783642086038: Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations

Edition présentée

ISBN 10 :  3642086039 ISBN 13 :  9783642086038
Editeur : Springer, 2010
Couverture souple