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Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation
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Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations Paperback - 2010

by M. I. Zelikin; S. a. Vakhrameev (Translator)


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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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  • Title Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations
  • Author M. I. Zelikin; S. a. Vakhrameev (Translator)
  • Binding Paperback
  • Edition Softcover reprin
  • Pages 284
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Date 2010-12-05
  • ISBN 9783642086038 / 3642086039
  • Weight 0.93 lbs (0.42 kg)
  • Dimensions 9.21 x 6.14 x 0.62 in (23.39 x 15.60 x 1.57 cm)
  • Dewey Decimal Code 515.64
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Control Theory and Optimization I : Homogeneous Spaces and the Riccati Equation in the Calculus of Variations

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

by S.A. Vakhrameev

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Paperback / softback. New. The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author's lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.
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Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Encyclopaedia of Mathematical Sciences, 86)

by Zelikin, M.I.

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