Infinite Dimensional Optimization and Control Theory
Published on 28. March 1999
Book
Hardback
816 pages
978-0-521-45125-3 (ISBN)
Description
This book is on existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from Kuhn-Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Evolution partial differential equations are studied using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.
Reviews / Votes
Review of the hardback: 'This outstanding monograph will be a great source both for experts and for graduate students interested in calculus of variations, non-linear programming, optimisation theory, optimal control and relaxation theory.' European Mathematical Society Review of the hardback: '... an impressive monograph on infinite dimensional optimal control theory. This is an original and extensive contribution which is not covered by other recent books in the control theory.' J. P. Raymond, Zentralblatt fuer MathematikMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
46 line figures
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 48 mm
Weight
1374 gr
ISBN-13
978-0-521-45125-3 (9780521451253)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Hector O. Fattorini
Infinite Dimensional Optimization and Control Theory
E-Book
07/2013
1st Edition
Cambridge University Press
€118.99
Available for download
Hector O. Fattorini
Infinite Dimensional Optimization and Control Theory
Book
06/2010
Cambridge University Press
€150.90
Shipment within 15-20 days
Person
Hector O. Fattorini graduated from the Licenciado en Matematica, Universidad de Buenos Aires in 1960 and gained a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences, New York University, in 1965. Since 1967, he has been a member of the Department of Mathematics at the University of California, Los Angeles.
Content
Part I. Finite Dimensional Control Problems: 1. Calculus of variations and control theory; 2. Optimal control problems without target conditions; 3. Abstract minimization problems: the minimum principle for the time optimal problem; 4. Abstract minimization problems: the minimum principle for general optimal control problems; Part II. Infinite Dimensional Control Problems: 5. Differential equations in Banach spaces and semigroup theory; 6. Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems; 7. Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations; 8. Interpolation and domains of fractional powers; 9. Linear control systems; 10. Optimal control problems with state constraints; 11. Optimal control problems with state constraints: The abstract parabolic case; Part III. Relaxed Controls: 12. Spaces of relaxed controls: topology and measure theory; 13. Relaxed controls in finite dimensional systems: existence theory; 14. Relaxed controls in infinite dimensional spaces: existence theory.