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Regulation of Control Systems

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

Abstract

In this chapter, we interpret viability theorems in the framework of control systems with a priori feedbacks 1 and state constraints.

Keywords

Lower Semicontinuous Differential Inclusion Viable Solution Open Loop Control Contingent 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.

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References

  1. [29]
    AUBIN J.-P., FRANKOWSKA H. (1990) Inclusions aux dérivées partielles gouvernant des contrôles de rétroaction, Comptes-Rendus de l’Académie des Sciences, Paris, 311, 851856Google Scholar
  2. [32]
    AUBIN J.-P.,FRANKOWSKA H. (to appear) Partial differential inclusions governing feedback controls,IIASA WP-90–028Google Scholar
  3. [31]
    AUBIN J.-P.,FRANKOWSKA H. (to appear) Hyperbolic systems of partial differential inclusions,IIASA WP-90–0Google Scholar
  4. [30]
    AUBIN J.-P., FRANKOWSKA H. (1990) Systèmes hyperboliques d’inclusions aux dérivées partielles, Comptes-Rendus de l’Académie des Sciences, Paris, 312, 271–276Google Scholar
  5. [19]
    AUBIN J.-P., DA PRATO G. (to appear) Contingent solutions to the center manifold equation,Annales de l’Institut Heanri-Poincaré, Analyse Non LinéaireGoogle Scholar
  6. [18]
    AUBIN J.-P., DA PRATO G. (1990) Solutions contingentes de l’équation de la variété centrale, Comptes-Rendus de l’Académie des Sciences, Paris, 311, 295–300Google Scholar
  7. [135]
    BYRNES C.I., ISIDORI A. (1990) Feedback design from the zero dynamics point of view, in COMPUTATION AND CONTROL, Bowers K., Lund J. Eds., Birkhäuser, 23–52Google Scholar
  8. [136]
    BYRNES C.I., ISIDORI A. (1990) Output regulation of nonlinear systems, IEEE Trans. Autom. Control, 35, 131–140Google Scholar
  9. [137]
    BYRNES C.I., ISIDORI A. (1990) Régulation asymptotique des systèmes non linéaires, Comptes-Rendus de l’Académie des Sciences, Paris, 309, 527–530Google Scholar
  10. [139]
    BYRNES C.I., ISIDORI A. (to appear) New methods for shaping the response of a nonlinear system,in NONLINEAR SYNTHESIS, Eds. Byrnes, Kurzhanski, BirkhäuserGoogle Scholar
  11. [250]
    FRANKOWSKA H. (1989) Non smooth solutions to an Hamilton-Jacobi equation, Proceedings of the International Conference Bellman Continuum, Antibes, France, June 1314, 1988, Lecture Notes in Control and Information Sciences, Springer VerlagGoogle Scholar
  12. [251]
    FRANKOWSKA H. (1989) Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equations,Applied Mathematics and Optimization, 19, 291–311Google Scholar
  13. [256]
    FRANKOWSKA H. (1991) Lower semicontinuous solutions to Hamilton-Jacobi equations,Cahiers de Mathématiques de la DécisionGoogle Scholar
  14. [193]
    CRANDALL M.G., LIONS P.L. (1983) Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277, 1–42Google Scholar
  15. [359]
    LIONS P.-L. (1982) GENERALIZED SOLUTIONS OF HAMILTONJACOBI EQUATIONS, Pitman, BostonGoogle Scholar
  16. [28]
    AUBIN J.-P., FRANKOWSKA H. (1990) SET-VALUED ANALYSIS, Birkhäuser, Systems and Control: Foundations and Applications Google Scholar
  17. [192]
    CRANDALL M.G., EVANS L.C., LIONS P.L. (1984) Some properties of viscosity solutions of Hamilton-Jacobi equation,Trans. Amer. Math. Soc., 282(2), 487–502Google 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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