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Viability Theory
ISBN-13:
9780817649104
Veröffentl:
2009
Seiten:
545
Autor:
Jean-Pierre Aubin
Serie:
Modern Birkhäuser Classics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory.
""The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis...The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." -Bulletin of the AMS"Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." -Mededelingen van het Wiskundig Genootschap"
Outline of the Book.- Viability Theorems for Ordinary and Stochastic Differential Equations.- Set-Valued Maps.- Viability Theorems for Differential Inclusions.- Viability Kernels and Exit Tubes.- Invariance Theorems for Differential Inclusions.- Regulation of Control Systems.- Smooth and Heavy Viable Solutions.- Partial Differential Inclusions of Tracking Problems.- Lyapunov Functions.- Miscellaneous Viability Issues.- Viability Tubes.- Functional Viability.- Viability Theorems for Partial Differential Inclusions.- Differential Games.
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