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基本説明
Examines viability theory and its applications to control theory and differential games.
Full Description
"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
Contents
Introduction.- Outline of the Book.- 1 Viability Theorems for Ordinary and Stochastic Differential Equations.- 2 Set-Valued Maps.- 3 Viability Theorems for Differential Inclusions.- 4 Viability Kernels and Exit Tubes.- 5 Invariance Theorems for Differential Inclusions.- 6 Regulation of Control Systems.- 7 Smooth and Heavy Viable Solutions.- 8 Partial Differential Inclusions of Tracking Problems.- 9 Lyapunov Functions.- 10 Miscellaneous Viability Issues.- 11 Viability Tubes.- 12 Functional Viability.- 13 Viability Theorems for Partial Differential Inclusions.- 14 Differential Games.- Bibliographical Comments.- Bibliography.- Index.
