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The Resource Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, by Martino Bardi, Italo Capuzzo-Dolcetta, (electronic resource)

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, by Martino Bardi, Italo Capuzzo-Dolcetta, (electronic resource)

Creator
Author
Contributor
Summary
This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems...will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." — Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises...Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." — ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." — Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." — Acta Applicandae Mathematicae
Language
  • eng
  • eng
Work
Publication
Edition
1st ed. 1997.
Extent
1 online resource (XVII, 574 p. 16 illus.)
Note
Bibliographic Level Mode of Issuance: Monograph
Contents
  • Outline of the main ideas on a model problem
  • Continuous viscosity solutions of Hamilton-Jacobi equations
  • Optimal control problems with continuous value functions: unrestricted state space
  • Optimal control problems with continuous value functions: restricted state space
  • Discontinuous viscosity solutions and applications
  • Approximation and perturbation problems
  • Asymptotic problems
  • Differential Games
Isbn
9780817647551
Instance
Label
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
Title
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
Statement of responsibility
by Martino Bardi, Italo Capuzzo-Dolcetta
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems...will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." — Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises...Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." — ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." — Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." — Acta Applicandae Mathematicae
Member of
http://library.link/vocab/creatorName
Bardi, Martino
Dewey number
519
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • s5IhDpH2bak
  • t95NGSOOAZk
Image bit depth
0
Language note
English
LC call number
  • Q295
  • QA402.3-402.37
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Capuzzo-Dolcetta, Italo.
Series statement
Modern Birkhäuser Classics,
http://library.link/vocab/subjectName
  • Systems theory
  • Mathematical optimization
  • Differential equations, partial
  • Systems Theory, Control
  • Optimization
  • Partial Differential Equations
Label
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, by Martino Bardi, Italo Capuzzo-Dolcetta, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Outline of the main ideas on a model problem -- Continuous viscosity solutions of Hamilton-Jacobi equations -- Optimal control problems with continuous value functions: unrestricted state space -- Optimal control problems with continuous value functions: restricted state space -- Discontinuous viscosity solutions and applications -- Approximation and perturbation problems -- Asymptotic problems -- Differential Games
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XVII, 574 p. 16 illus.)
File format
multiple file formats
Form of item
online
Isbn
9780817647551
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4755-1
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000777928
  • (SSID)ssj0000325405
  • (PQKBManifestationID)11243690
  • (PQKBTitleCode)TC0000325405
  • (PQKBWorkID)10320948
  • (PQKB)10693686
  • (DE-He213)978-0-8176-4755-1
  • (MiAaPQ)EBC3072302
  • (EXLCZ)991000000000777928
Label
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, by Martino Bardi, Italo Capuzzo-Dolcetta, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Outline of the main ideas on a model problem -- Continuous viscosity solutions of Hamilton-Jacobi equations -- Optimal control problems with continuous value functions: unrestricted state space -- Optimal control problems with continuous value functions: restricted state space -- Discontinuous viscosity solutions and applications -- Approximation and perturbation problems -- Asymptotic problems -- Differential Games
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XVII, 574 p. 16 illus.)
File format
multiple file formats
Form of item
online
Isbn
9780817647551
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4755-1
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)1000000000777928
  • (SSID)ssj0000325405
  • (PQKBManifestationID)11243690
  • (PQKBTitleCode)TC0000325405
  • (PQKBWorkID)10320948
  • (PQKB)10693686
  • (DE-He213)978-0-8176-4755-1
  • (MiAaPQ)EBC3072302
  • (EXLCZ)991000000000777928

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