Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource (xv, 798 pages) , digital, PDF file(s).

ISBN: 9780511574795

Series Statement: Encyclopedia of mathematics and its applications volume 62

Content: 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.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015) , pt. 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. The Minimum Principle for General Optimal Control Problems -- pt. II. Infinite Dimensional Control Problems. 5. Differential Equations in Banach Spaces and Semigroup Theory. 6. Abstract Minimization Problems in Hilbert Spaces. 7. Abstract Minimization Problems in Banach Spaces. 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 -- pt. III. Relaxed Controls.

Additional Edition: ISBN 9780521154543

Additional Edition: ISBN 9780521451253

Additional Edition: ISBN 9780521451253

Additional Edition: ISBN 9780521154543

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780521451253

Language: English

DOI: 10.1017/CBO9780511574795

URL: Volltext

URL: Inhaltstext

UID:

Format: 1 online resource (xv, 798 pages) : , digital, PDF file(s).

ISBN: 9780511574795 (ebook)

Series Statement: Encyclopedia of mathematics and its applications ; volume 62

Content: 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.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , 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. , 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. , Abstract Minimization Problems in Banach Spaces. , Interpolation and Domains of Fractional Powers. , Linear Control Systems. , Optimal Control Problems with State Constraints. , Optimal Control Problems with State Constraints -- , Relaxed Controls.

Additional Edition: Print version: ISBN 9780521451253

Language: English

URL: https://doi.org/10.1017/CBO9780511574795

UID:

Format: 1 online resource (xv, 798 pages) : , digital, PDF file(s).

ISBN: 1-139-88648-7 , 1-107-10301-0 , 1-107-08858-5 , 1-107-10053-4 , 1-107-09476-3 , 0-511-57479-7

Series Statement: Encyclopedia of mathematics and its applications ;

Content: 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.

Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , pt. I. Finite dimensional control problems -- pt. II. Infinite dimensional control problems -- pt. III. Relaxed controls. , English

Additional Edition: ISBN 0-521-15454-5

Additional Edition: ISBN 0-521-45125-6

Language: English