Modern Birkhäuser Classics

Viability Theory

Authors: Aubin, Jean-Pierre

  • This is an affordable new soft cover edition of a classic text
  • Provides a wide scope that makes the text and ideal reference for anyone encountering problems related to viability theory in their research
  • Offers an essentially self-contained presentation
  • Minimal prerequisites required are basic graduate courses in modern analysis and functional analysis
  • Aimed at a broad audience of graduate students, researchers, and practitioners in pure and applied mathematics, systems/control, artificial intelligence, economics, game theory, theoretical biology, population genetics, and cognitive sciences
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4910-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this book

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.

Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplines—artificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciences—to go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment.

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

Table of contents (16 chapters)

  • Introduction

    Aubin, Jean-Pierre

    Pages 1-9

  • Outline of the Book

    Aubin, Jean-Pierre

    Pages 11-17

  • Viability Theorems for Ordinary and Stochastic Differential Equations

    Aubin, Jean-Pierre

    Pages 19-52

  • Set-Valued Maps

    Aubin, Jean-Pierre

    Pages 53-75

  • Viability Theorems for Differential Inclusions

    Aubin, Jean-Pierre

    Pages 77-118

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4910-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Viability Theory
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-4910-4
DOI
10.1007/978-0-8176-4910-4
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XXV, 545
Additional Information
Originally published in the series: Systems & Control: Foundations & Applications
Topics