Viability Theory

  • Jean-Pierre Aubin

Part of the Systems & Control: Foundations & Applications book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Jean-Pierre Aubin
    Pages 1-9
  3. Jean-Pierre Aubin
    Pages 11-17
  4. Jean-Pierre Aubin
    Pages 53-75
  5. Jean-Pierre Aubin
    Pages 77-118
  6. Jean-Pierre Aubin
    Pages 119-155
  7. Jean-Pierre Aubin
    Pages 157-198
  8. Jean-Pierre Aubin
    Pages 199-234
  9. Jean-Pierre Aubin
    Pages 235-273
  10. Jean-Pierre Aubin
    Pages 315-350
  11. Jean-Pierre Aubin
    Pages 351-375
  12. Jean-Pierre Aubin
    Pages 377-399
  13. Jean-Pierre Aubin
    Pages 401-423
  14. Jean-Pierre Aubin
    Pages 451-484
  15. Back Matter
    Pages 485-545

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


Nonlinear system Optimization Methods Stochastic Differential Equations Tracking artificial intelligence construction control control system differential equation fuzzy fuzzy control game theory genetics kernel optimization

Authors and affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.EDOMADE (Ecole Doctorale de Mathématique de la Décision)Université de Paris-DauphineParis cedex 16France

Bibliographic information