Control Theory and Optimization: Vol.1 Control Theory and Optimization I
(Sprache: Englisch)
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...
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Produktinformationen zu „Control Theory and Optimization: Vol.1 Control Theory and Optimization I “
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.
Klappentext zu „Control Theory and Optimization: Vol.1 Control Theory and Optimization I “
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.Inhaltsverzeichnis zu „Control Theory and Optimization: Vol.1 Control Theory and Optimization I “
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.
Bibliographische Angaben
- Autor: M.I. Zelikin
- 2000, 284 Seiten, mit zahlreichen Abbildungen, Maße: 15,9 x 24,1 cm, Gebunden, Englisch
- Übersetzung:Vakhrameev, S.A.
- Verlag: Springer
- ISBN-10: 3540667415
- ISBN-13: 9783540667414
- Erscheinungsdatum: 15.12.1999
Sprache:
Englisch
Rezension zu „Control Theory and Optimization: Vol.1 Control Theory and Optimization I “
"[...] Der sehr gut lesbare Band beruht auf Vorlesungen des Autors an der Universität Moskau für Studierende höherer Semester und ist sowohl für das Selbststudium als auch als Grundlage für Vorlesungen geeignet." Internationale Mathematische Nachrichten 188, S. 63, 2001.... 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 Rezension, Vol. 43/1, March.
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