Jean-Pierre Aubin

Viability Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

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)

Produktdetails

• Verlag: Birkhäuser Boston
• Erscheinungstermin: 28. Mai 2009
• Englisch
• ISBN-13: 9780817649104
• Artikelnr.: 43727921

Inhaltsangabe

Outline of the Book.- Viability Theorems for Ordinary and Stochastic Differential Equations.- Set-Valued Maps.- Viability Theorems for Differential Inclusions.- Viability Kernels and Exit Tubes.- Invariance Theorems for Differential Inclusions.- Regulation of Control Systems.- Smooth and Heavy Viable Solutions.- Partial Differential Inclusions of Tracking Problems.- Lyapunov Functions.- Miscellaneous Viability Issues.- Viability Tubes.- Functional Viability.- Viability Theorems for Partial Differential Inclusions.- Differential Games.

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Viability Kernels and Examples.- Mathematical Properties of Viability Kernels.- First-Order Partial Differential Equations.- Appendices.

Rezensionen

From the reviews of the second edition:

"This comprehensive book of more than 800 pages has many purposes. ... who want to learn the theory and may be interested in its research potential will also be quite happy with the book. ... authors have made their book very lively by providing quotations and pictures of famous scientists and writers ... . great reference for many types of readers: mathematicians, application-oriented users, and even science historians interested in the evolution of science and its cultural aspects. It will certainly motivate young scientists ... ." (Alain Bensoussan, Mathematical Reviews, January, 2011)

"This is the second edition of the well-known monograph. It is devoted to the viability theory and algorithmic methods for investigation of the adaptation of complex systems with uncertainties. Such systems can be found in biology, economics, environmental sciences, final markets, control theory, robotics etc. ... The monograph contains many unpublished results and is addressed to graduate students and scientists." (Tadeusz Kaczorek, Zentralblatt MATH, Vol. 1238, 2012)