Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Encyclopaedia of Mathematical Sciences, 86, Band 86) - Hardcover

Buch 20 von 47: Encyclopaedia of Mathematical Sciences

Zelikin, M.I.

 
9783540667414: Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Encyclopaedia of Mathematical Sciences, 86, Band 86)
Hardcover
ISBN 10: 3540667415 ISBN 13: 9783540667414
Verlag: Springer, 1999

Inhaltsangabe

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.

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Verlag
Springer
Erscheinungsdatum
1999
Sprache
Englisch
ISBN 10 
3540667415
ISBN 13 
9783540667414
Einband
Gebundene Ausgabe
Anzahl der Seiten
296
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