Control Theory and Optimization I (Hardcover)

M.I. Zelikin

ISBN 10: 3540667415 / ISBN 13: 9783540667414

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1999

About this Item

Hardcover. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Seller Inventory # 9783540667414

Bibliographic Details

• Title: Control Theory and Optimization I (Hardcover)
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Publication Date: 1999
• Language: English
• ISBN 10: 3540667415
• ISBN 13: 9783540667414
• Binding: Hardcover
• Condition: new

About this title

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.

Review

".... This book was written by a master expositor and is required reading for anyone who is intersted in pursuing a serious study of the Riccati equation. The first four chapters should be required reading for every graduate student who is thinking about studying geometric or mathematical control theory. I do not know of a better overview of the matheamtics required to do modern geometric control theory. Every control theorist should have a well-worn copy of this book on his bookshelf. ... Zelikin has written a book that will be well read for many years...."

Siam Review, Vol. 43/1, March 2001

"... The text requires good background, but will be a useful reference."

Mathematika 2002, Issue 93-94