Infinite Dimensional Optimization and Control Theory

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Cambridge University Press, Mar 28, 1999 - Mathematics - 798 pages
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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.
 

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Contents

Calculus of Variations and Control Theory
3
Hypersonic Flow
17
Optimal Control Problems Without Target Conditions
26
The Minimum Principle
84
The Minimum Principle for General Optimal Control Problems
122
Nose Shape Problem
151
Differential Equations in Banach Spaces and Semigroup Theory
169
Abstract Minimization Problems in Hilbert Spaces
251
Interpolation and Domains of Fractional Powers
385
Linear Control Systems
426
Optimal Control Problems with State Constraints
474
Optimal Control Problems with State Constraints
509
Spaces of Relaxed Controls Topology and Measure Theory
603
Relaxed Controls in Finite Dimensional Systems
674
Relaxed Controls in Infinite Dimensional Systems
709
References
773

Variational Equation
262
Abstract Minimization Problems in Banach Spaces
310

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Common terms and phrases

Popular passages

Page 793 - Regularity and stability for the mathematical programming problem in Banach spaces.
Page 779 - The time-optimal problem for boundary control of the heat equation. Calculus of Variations and Control Theory (DL Russell, Ed.) Academic Press (1976) 305-320.
Page 779 - Fattorini, A unified theory of necessary conditions for nonlinear nonconvex control systems, Appl. Math.
Page 773 - Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space.
Page 773 - Finite-time null controllability for a class of linear evolution equations on a Banach space with control constraints, /. Optimization Theory & Appl.
Page 773 - Convergence of finite element approximations to state constrained convex parabolic boundary control problems, SIAM J.

About the author (1999)

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.