Control Theory and Optimization I

Homogeneous Spaces and the Riccati Equation in the Calculus of Variations

Häftad, Engelska, 2010

Av M.I. Zelikin, M. I. Zelikin

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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.

Produktinformation

Utgivningsdatum2010-12-05
Mått155 x 235 x 17 mm
Vikt453 g
FormatHäftad
SpråkEngelska
SerieEncyclopaedia of Mathematical Sciences
Antal sidor284
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783642086038
ÖversättareVakhrameev, S.A., Vakhrameev, S. a., Vakhrameev, S. A.

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik
Optimering inom Naturvetenskap och teknik

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.

"... 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