Infinite Dimensional Optimization and Control Theory (Encyclopedia of Mathematics and its Applications)

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9780521451253: Infinite Dimensional Optimization and Control Theory (Encyclopedia of Mathematics and its Applications)
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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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Book Description:

This book treats optimal problems for systems described by ordinary and partial differential equations, using an approach that unifies finite dimensional and infinite dimensional nonlinear programming. Problems include control and state constraints and target conditions. Applications of the theory include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.Although written at a level suitable for beginning graduate students in applied mathematics this comprehensive treatment will also be a valuable reference for researchers in control theory.

About the Author:

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

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9780521154543: Infinite Dimensional Optimization and Control Theory (Encyclopedia of Mathematics and its Applications)

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2009. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # APC9780521451253

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2009. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # APC9780521451253

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