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Exact controllability in short time

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Book cover Control of Boundaries and Stabilization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 125))

Abstract

The Hilbert Uniqueness Method, introduced by J.-L. Lions, allows one to obtain explicit estimates for the minimal time of exact controllability. We present here a constructive method to improve these estimates. It is based on a slightly more precise form of the usual a priori estimates in the HUM method and on an estimation method introduced recently (for different purposes) by A. Haraux.

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References

  1. A. Haraux, Quelques propriétés des séries lacunaires utiles dans l'étude des vibrations élastiques, Res. Notes in Math., H. Brézis and J.-L. Lions editors, Nonlinear Partial Differential Equations and Their Applications, Collège de France seminar, 1987–88, Pitman, to appear.

    Google Scholar 

  2. L. F. Ho, Observabilité frontière de l'équation des ondes, C. R. Acad. Sci. Paris Sér. I Math. 302(1986), 443–446.

    MATH  Google Scholar 

  3. V. Komornik, Contrôlabilité exacte en un temps minimal, C. R. Acad. Sci. Paris Sér. I Math. 304(1987), 223–225.

    MathSciNet  MATH  Google Scholar 

  4. V. Komornik, Exact controllability in short time for the wave equation, Ann. Inst. H. Poincaré, Anal. Nonlinéaire, to appear.

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  5. V. Komornik, Une méthode générale pour la contrôlabilité exacte en temps minimal, C. R. Acad. Sci. Paris Sér. I Math., to appear.

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  6. V. Komornik, Contrôlabilité exacte en temps minimal de quelques modèles de plaques, C. R. Acad. Sci. Paris Sér. I Math., to appear.

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  7. V. Komornik, A general method of exact controllability in short time and applications, to appear.

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  8. J. E. Lagnese and J.-L. Lions, Modelling, Analysis and Control of Thin Plates, Masson, Collection R. M. A., Paris, 1988.

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  9. J.-L. Lions, Contrôlabilité exacte des systèmes distribués, C. R. Acad. Sci. Paris Sér. I Math. 302(1986), 471–475.

    MATH  Google Scholar 

  10. J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev. 30(1988), 1–68.

    Article  MathSciNet  MATH  Google Scholar 

  11. J.-L. Lions, Contrôlabilité exacte des systèmes distribués, I–II, Masson, Collection R. M. A., Paris, 1988.

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  12. J.-L. Lions, Contrôlabilité exacte et perturbations singulières (II). La méthode de dualité, to appear.

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  13. E. Zuazua, Contrôlabilité exacte d'une modèle de plaques en un temps arbitrairement petit, C. R. Acad. Sci. Paris Sér. I Math. 304(1986), 173–176.

    MathSciNet  Google Scholar 

  14. E. Zuazua, Contrôlabilité exacte de quelques modèles de plaques en un temps arbitrairement petit, Appendix in J.-L. Lions (3).

    Google Scholar 

  15. E. Zuazua, Some remarks on the boundary stabilizability of the wave equation, in Control of boundaries and stabilization, J. Simon editor, Lecture Notes in Control and Information Sciences, Springer-Verlag, 1989.

    Google Scholar 

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Jacques Simon

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© 1989 International Federation for Information Processing

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Komornik, V. (1989). Exact controllability in short time. In: Simon, J. (eds) Control of Boundaries and Stabilization. Lecture Notes in Control and Information Sciences, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043358

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  • DOI: https://doi.org/10.1007/BFb0043358

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51239-4

  • Online ISBN: 978-3-540-46181-4

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