Viability Theory
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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.
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
This soft cover edition of a classic text examines viability theory and its applications to control theory and differential games. It emphasizes the construction of feedbacks and dynamical systems by myopic optimization methods.
"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
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
Autor*in
Jean-Pierre Aubin
Themen in »Viability Theory«
Nonlinear system Optimization Methods Stochastic Differential Equations Tracking artificial intelligence construction control control system differential equation fuzzy fuzzy control game theory genetics kernel optimization
Stimmen zu »Viability Theory«
From the reviews:
"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)
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