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Miscellaneous Viability Issues

  • Jean-Pierre Aubin
Part of the Systems & Control: Foundations & Applications book series (MBC)

Abstract

This chapter gathers several topics which can be studied from the viability point of view:
  1. 1.

    — How to correct a differential inclusion to make a given closed subset a viability domain (variational differential inequalities)

     
  2. 2.

    — How to describe situations where some evolutions are more likely to be implemented than others (fuzzy viability)

     
  3. 3.

    — How to approximate viable solutions to differential inclusions (finite-difference schemes) and their equilibria (Newton’s method).

     

Keywords

Membership Function Lower Semicontinuous Differential Inclusion Fuzzy Subset Viable Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [84]
    BENSOUSSAN A., LIONS J.L (1982) CONTRÔLE IMPULSIONNEL ET INÉQUATIONS QUASI-VARIATIONNELLES, Dunod, ParisGoogle Scholar
  2. [275]
    HENRY D. (1981) GEOMETRIC THEORY OF SEMILINEAR PARABOLIC EQUATIONS, Springer-Verlag, Lecture Notes in Mathematics, 840MATHGoogle Scholar
  3. [187]
    CORNET B. (1976) On planning procedures defined by multi-valued differential equations,Système dynamiques et modèles économiques (C.N.R.S)Google Scholar
  4. [189]
    CORNET B. (1983) An existence theorem of slow solutions for a class of differential inclusions Google Scholar
  5. [190]
    CORNET B. (1983) Monotone dynamic processes in a pure exchange economy Google Scholar
  6. [305]
    KRIVAN V. (to appear) G-projection of differential inclusions,preprintGoogle Scholar
  7. [58]
    AUBIN J.-P. (1990) Fuzzy differential inclusions,Problems of Control and Information Theory, 19, 55–67Google Scholar
  8. [538]
    ZADEH L.A. (1965) Fuzzy sets,Information and Control, 8, 338–353Google Scholar
  9. [9]
    DUBOIS D., PRADE H. (to appear) Toll sets, 4th IFSA World Congress, Brussels, 1991Google Scholar
  10. [221]
    DUBOIS D., PRADE H. (1987) On several definitions of the differential of a fuzzy mapping, Fuzzy sets and systems journal, 24, 117–120Google Scholar
  11. [287]
    KALEVA O. (1987) Fuzzy differential equations,Fuzzy sets and systems journal, 24, 301–317Google Scholar
  12. [111]
    BOBYLEV V.N. (1990) A possibilistic argument for irreversibility, Fuzzy sets and systems, 34, 73–80CrossRefMATHMathSciNetGoogle Scholar
  13. [220]
    DUBOIS D., PRADE H. (1980) FuzzY SETS AND SYSTEMS - THEORY AND APPLICATIONS, Academic PressGoogle Scholar
  14. [461]
    SAINT-PIERRE P. (1987) Approximation de solutions lentes d’inclusions différentielles,(Preprint)Google Scholar
  15. [508]
    VELIOV V. M. (1989) Approximations to differential inclusions by discrete inclusions,IIASA WP 89–017Google Scholar
  16. [509]
    VELIOV V. M. (1989) Second order discrete approximations to strongly convex differential inclusions, Systems Control Letters, 13, 263–269Google Scholar
  17. [510]
    VELIOV V. M. (1989) Discrete approximations of integrals of multivalued mappings, C. R. Acad. Sc. Bulgares, 42, 51–54Google Scholar
  18. [511]
    VELIOV V. M. (to appear) Second order discrete approximations to linear differential inclusions Google Scholar
  19. [462]
    SAINT-PIERRE P. (to appear) Newton’s method for set-valued maps,Cahiers de Mathématiques de la DécisionGoogle Scholar
  20. [513]
    WAZEWSKI T. (1947) Sur l’évaluation du domaine d’existence des fonctions implicites réelles ou complexes,Ann. Soc. Polon. Math.,20, 81–120Google Scholar
  21. [392]
    OLECH C., PARTHASARATHY T.,RAVINDRAN G. (1990) Almost N-matrices and its applications to linear complementary problem and global univalence,Core discus. paper 9014Google Scholar

Copyright information

© Springer Science+Business Media New York 2009

Authors and Affiliations

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

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