Infinite Dimensional Optimization and Control Theory

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Hardcover | 2 August 1999

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816 Pages

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23.39 x 15.6 x 4.29

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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.

Industry Reviews

'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 '... 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

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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.

Infinite Dimensional Optimization and Control Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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