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Infinite Dimensional Optimization and Control Theory : Encyclopedia of Mathematics and Its Applications - Hector O. Fattorini

Infinite Dimensional Optimization and Control Theory

Encyclopedia of Mathematics and Its Applications


Published: 24th June 2010
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This book concerns existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations.

The author obtains these necessary conditions from Kuhn-Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Fattorini studies evolution partial differential equations using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory.

The author establishes existence of optimal controls 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.

  • Unifies finite and infinite dimensional control problems
  • Deals with the important problems of target conditions and state constraints.
About the Author

Hector O. Fattorini graduated from the Licenciado en Matemática, 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.

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 fur Mathematik

Finite Dimensional Control Problems
Calculus of variations and control theory
Optimal control problems without target conditions
Abstract minimization problems: the minimum principle for the time optimal problem
Abstract minimization problems: the minimum principle for general optimal control problems
Infinite Dimensional Control Problems
Differential equations in Banach spaces and semigroup theory
Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems
Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations
Interpolation and domains of fractional powers
Linear control systems
Optimal control problems with state constraints
Optimal control problems with state constraints: The abstract parabolic case
Relaxed Controls
Spaces of relaxed controls: topology and measure theory
Relaxed controls in finite dimensional systems: existence theory
Relaxed controls in infinite dimensional spaces: existence theory
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521154543
ISBN-10: 0521154545
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 816
Published: 24th June 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.4 x 15.6  x 4.1
Weight (kg): 1.12