Advertisement

Invariance Theorems for Differential Inclusions

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

Abstract

We devote this chapter to subsets invariant under a set-valued map, to invariance domains, kernels and envelopes, and to some of their properties.

Keywords

Closed Subset Lower Semicontinuous Differential Inclusion Tangent Cone Closed Convex Cone 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [113]
    BOULIGAND G. (1932) INTRODUCTION À LA GÉOMÉTRIE INFINITÉSIMALE DIRECTE, Gauthier-VillarsGoogle Scholar
  2. [114]
    BOULIGAND G. (1932) Sur la semi-continuité d’inclusions et quelques sujets connexes,Enseignement Mathématique, 31, 14–22Google Scholar
  3. [371]
    MARCHAUD H. (1934) Sur les champs de demi-cônes et les équations différentielles du premier ordre,Bull. Sc. Math., 62, 1–38Google Scholar
  4. [166]
    CROQUET G. (1947) Convergences,Annales de l’ Univ. de Grenoble, 23, 55–112Google Scholar
  5. [540]
    ZAREMBA S.C. (1936) Sur les équations au paratingent,Bull. Sc. Math., 60, 139–160Google Scholar
  6. [374]
    MARTIN R.M. (1976) Nonlinear operators and differential equations in Banach spaces, Wiley Interscience, New YorkMATHGoogle Scholar
  7. [17]
    AUBIN J.-P., CLARKE (1977) Monotone invariant solutions to differential inclusions, J. London Math. Soc., 16, 357–366Google Scholar
  8. [28]
    AUBIN J.-P., FRANKOWSKA H. (1990) SET-VALUED ANALYSIS, Birkhäuser, Systems and Control: Foundations and Applications Google Scholar
  9. [46]
    AUBIN J.-P. (1982) Comportement lipschitzien des solutions de problèmes de minimisation convexes,Comptes-Rendus de l’Académie des Sciences, PARIS, 295, 235–238Google Scholar
  10. [446]
    ROCKAFELLAR R.T. (1979) Clarke’s tangent cones and the boundaries of closed sets in Rn,Nonlinear Anal. Theor. Math. Appl., 3, 145–154Google Scholar
  11. [26]
    AUBIN J.-P., FRANKOWSKA H. (1987) On the inverse function theorem, J. Math. Pures Appliquées, 66, 71–89Google Scholar
  12. [368]
    MADERNER N. (to appear) Regulation of control systems under inequality viability constraints Google Scholar
  13. [257]
    FRANKOWSKA H. (1992) CONTROL OF NONLINEAR SYSTEMS AND DIFFERENTIAL INCLUSIONS, Birkhäuser, Systems and Control: Foundations and Applications Google Scholar
  14. [229]
    FILIPPOV A.F. (1967) Classical solutions of differential equations with multivalued right hand side,SIAM J. on Control, 5, 609–621Google Scholar
  15. [172]
    CLARKE F.H. (1975) Generalized gradients and applications,Trans. Am. Math. Soc., 205, 247–262Google Scholar
  16. [430]
    QUINCAMPOIX M. (1990) Frontières de domaines d’invariance et de viabilité pour des inclusions différentielles avec contraintes,Comptes-Rendus de l’Académie des Sciences, Paris, 311, 411–416Google Scholar
  17. [431]
    QUINCAMPOIX M. (1990) Playable differentiable games, J. Math. Anal. Appl.Google Scholar
  18. [432]
    QUINCAMPOIX M. (1991) Differential inclusions and target problems,SIAM J. Control,Optimization, IIASA WP-90Google Scholar
  19. [434]
    QUINCAMPOIX M. (to appear) Enveloppes d’invariance,Cahiers de Mathématiques de la décisionGoogle Scholar
  20. [14]
    AUBIN J.-P., FRANKOWSKA H., OLECH C. (1986) Controllability of convex processes, SIAM J. of Control and Optimization, 24, 1192–1211Google Scholar
  21. [15]
    AUBIN J.-P., FRANKOWSKA H., OLECH C. (1986) Contrôlabilité des processus convexes, Comptes-Rendus de l’Académie des Sciences, Paris, 301, 153–156Google Scholar
  22. [254]
    FRANKOWSKA H. (1990) On controllability and observability of implicit systems,Systems and Control Letters, 14, 219–225Google Scholar
  23. [22]
    AUBIN J.-P., EKELAND I. (1984) APPLIED NONLINEAR ANALYSIS, Wiley-InterscienceGoogle 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

Personalised recommendations