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Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations
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Catalogue Information
Field name
Details
Dewey Class
516.36
Title
Control Theory and Optimization I ([EBook]) : Homogeneous Spaces and the Riccati Equation in the Calculus of Variations / by M. I. Zelikin.
Author
Zelikin, Mikhail Ilich
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer , 2000.
Physical Details
XII, 284 pages : online resource.
Series
Encyclopaedia of mathematical sciences
0938-0396 ; ; 86
ISBN
9783662041369
Summary Note
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.:
Contents note
1. Classical Calculus of Variations -- 2. Riccati Equation in the Classical Calculus of Variations -- 3. Lie Groups and Lie Algebras -- 4. Grassmann Manifolds -- 5. Matrix Double Ratio -- 6. Complex Riccati Equations -- 7. Higher-Dimensional Calculus of Variations -- 8. On the Quadratic System of Partial Differential Equations Related to the Minimization Problem for a Multiple Integral -- Epilogue -- Appendix to the English Edition -- References.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-662-04136-9
Links to Related Works
Subject References:
Calculus of variations
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Calculus of variations and optimal control; optimization
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Differential Geometry
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Mathematics
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Authors:
Zelikin, Mikhail Ilich
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Zelikin, Mikhail Ilich
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Corporate Authors:
SpringerLink (Online service)
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Series:
Encyclopaedia of mathematical sciences
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Classification:
516.36
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