Authors:
- An affordable new softcover edition of a classic text
- Wide scope makes the book an ideal reference for anyone encountering problems related to viability theory in their research
- Essentially self-contained presentation
- Minimal prerequisites: basic graduate courses in modern analysis and functional analysis
- Aimed at a broad audience of graduate students, researchers, and practitioners in pure/applied mathematics, systems/control, artificial intelligence, economics, game theory, theoretical biology, population genetics, and cognitive sciences
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
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)
Authors and Affiliations
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EDOMADE (Ecole Doctorale de Mathématique de la Décision), Université de Paris-Dauphine, Paris cedex 16, France
Jean-Pierre Aubin
Bibliographic Information
Book Title: Viability Theory
Authors: Jean-Pierre Aubin
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-0-8176-4910-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2009
eBook ISBN: 978-0-8176-4910-4Published: 28 May 2009
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XXV, 545
Additional Information: Originally published in the series: Systems & Control: Foundations & Applications
Topics: Systems Theory, Control, Control, Robotics, Mechatronics, Game Theory, Economics, Social and Behav. Sciences, Mathematical and Computational Biology, Artificial Intelligence