Viability Theory (Systems & Control: Foundations & Applications)

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 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)

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the Main Purpose Of Viability Theory Is To Explain The Viable Evolution Of Systems By Revealing The Concealed Feedbacks Which Allow The System To Be Regulated And Provide Selection Mechanisms For Implementing Them. The Theory Allows Researchers In Artificial Intelligence, Economics, Game Theory, Theoretical Biology, Population Genetics, Ethology, Cognitive Sciences, Etc., To Go Beyond Deterministic Models By Studying Systems In A Dynamical Or Evolutionary Perspective In An Uncertain Environment. Annotation C. Book News, Inc., Portland, Or (booknews.com)

Front Matter....Pages i-xxv Introduction....Pages 1-9 Outline of the Book....Pages 11-17 Viability Theorems for Ordinary and Stochastic Differential Equations....Pages 19-52 Set-Valued Maps....Pages 53-75 Viability Theorems for Differential Inclusions....Pages 77-118 Viability Kernels and Exit Tubes....Pages 119-155 Invariance Theorems for Differential Inclusions....Pages 157-198 Regulation of Control Systems....Pages 199-234 Smooth and Heavy Viable Solutions....Pages 235-273 Partial Differential Inclusions of Tracking Problems....Pages 275-314 Lyapunov Functions....Pages 315-350 Miscellaneous Viability Issues....Pages 351-375 Viability Tubes....Pages 377-399 Functional Viability....Pages 401-423 Viability Theorems for Partial Differential Inclusions....Pages 425-450 Differential Games....Pages 451-484 Back Matter....Pages 485-545 Examines viability theory and its applications to control theory and differential games. This book emphasises the construction of feedbacks and dynamical systems by myopic optimization methods. It is suitable for graduate students and research mathematicians 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.