Partial Differential Inclusions of Tracking Problems

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


Consider two finite dimensional vector-spaces X and Y, two set-valued maps F: X × YX, G: X × YY and the system of differential inclusions


Differential Inclusion Tracking Problem Graphical Limit Contingent Derivative Viability Kernel 
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  1. [58]
    AUBIN J.-P. (1990) Fuzzy differential inclusions,Problems of Control and Information Theory, 19, 55–67Google Scholar
  2. [84]
  3. [111]
    BOBYLEV V.N. (1990) A possibilistic argument for irreversibility, Fuzzy sets and systems, 34, 73–80CrossRefMATHMathSciNetGoogle Scholar
  4. [187]
    CORNET B. (1976) On planning procedures defined by multi-valued differential equations,Système dynamiques et modèles économiques (C.N.R.S)Google Scholar
  5. [189]
    CORNET B. (1983) An existence theorem of slow solutions for a class of differential inclusions Google Scholar
  6. [190]
    CORNET B. (1983) Monotone dynamic processes in a pure exchange economy Google Scholar
  7. [220]
    DUBOIS D., PRADE H. (1980) FuzzY SETS AND SYSTEMS - THEORY AND APPLICATIONS, Academic PressGoogle Scholar
  8. [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
  9. [222]
    DUBOIS D., PRADE H. (to appear) Toll sets, 4th IFSA World Congress, Brussels, 1991Google Scholar
  10. [275]
    HENRY D. (1981) GEOMETRIC THEORY OF SEMILINEAR PARABOLIC EQUATIONS, Springer-Verlag, Lecture Notes in Mathematics, 840MATHGoogle Scholar
  11. [287]
    KALEVA O. (1987) Fuzzy differential equations,Fuzzy sets and systems journal, 24, 301–317Google Scholar
  12. [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
  13. [461]
    SAINT-PIERRE P. (1987) Approximation de solutions lentes d’inclusions différentielles,(Preprint)Google Scholar
  14. [462]
    SAINT-PIERRE P. (to appear) Newton’s method for set-valued maps,Cahiers de Mathématiques de la DécisionGoogle 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. [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
  20. [538]
    ZADEH L.A. (1965) Fuzzy sets,Information and Control, 8, 338–353Google 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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