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The euler-bernoulli plate is exactly controllable via bending moments only

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Optimal Control of Partial Differential Equations

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 149))

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This material is based upon work supported under a National Science Foundation Graduate Fellowship.

Research partially supported by National Science Foundation under Grant DMS-87-96320 and by Air Force Office of Scientific Research under Grant AFOSR-87-0321.

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References

  1. P. Grisvard. "Caracterization de quelques espaces d'interpolation", Arch. Rational Mech. Anal., 25 (1967), pp. 40–63.

    Google Scholar 

  2. J. L. Lions. Contrôlabilité exacte de systèmes distribués, Masson, Paris, 1988.

    Google Scholar 

  3. I. Lasiecka. "Exact controllability of a plate equation with one control acting as a bending moment", Mercel Dekker, (to appear).

    Google Scholar 

  4. G. Lebeau. "Controle de l'equation de Schrödinger", Report Universite de Paris-Sud Mathematiques, 1989.

    Google Scholar 

  5. F. Flandoli, I. Lasiecka and R. Triggiani. "Algebraic Riccati Equations with nonsmooth observation arising in hyperbolic and Euler-Bernoulli equations", Annali di Math. Pura Appl. (IV) 25 (1988), pp. 307–382.

    Google Scholar 

  6. J. Lagnese and J. L. Lions. Modelling, Analysis and Control of Thin Plates, Masson, Paris, 1988.

    Google Scholar 

  7. I. Lasiecka and R. Triggiani. "Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions: a nonconservative case", SIAM J. Control Optim. 27 (1989), pp. 330–373.

    Google Scholar 

  8. I. Lasiecka and R. Triggiani. "Exact controllability of the Euler-Bernoulli equation with boundary controls for displacement and moment", J. Math. Anal. Appl., 146, No. 1 (1990), pp. 1–33.

    Google Scholar 

  9. I. Lasiecka and R. Triggiani. "Exact controllability and uniform stabilization of Kirchoff plates with boundary control only on Δw|Σ and homogeneous boundary displacement", J. Differential Equations, (to appear).

    Google Scholar 

  10. I. Lasiecka and R. Triggiani. Further results on exact controllability of the Euler-Bernoulli equation with controls on the Dirichlet and Neumann boundary conditions, in "Lecture Notes in Control and Information Sciences", Proceedings of Conference on Stabilization of Flexible Structures, Springer-Verlag, (to appear).

    Google Scholar 

  11. I. Lasiecka and R. Triggiani. "Exact controllability and uniform stabilization of Euler-Bernoulli equations with boundary control only in Δw|Σ", Boll. Un. Mat. Ital., (to appear).

    Google Scholar 

  12. I. Lasiecka and R. Triggiani. "Regularity theory for a class of nonhomogeneous Euler-Bernoulli equations: a cosine operator approach", Boll. Un. Mat. Ital. (7), 3-B (1989), pp.199–228.

    Google Scholar 

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Karl-Heinz Hoffmann Werner Krabs

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© 1991 International Federation for Information Processing

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Ann Horn, M., Lasiecka, I. (1991). The euler-bernoulli plate is exactly controllable via bending moments only. In: Hoffmann, KH., Krabs, W. (eds) Optimal Control of Partial Differential Equations. Lecture Notes in Control and Information Sciences, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043220

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  • DOI: https://doi.org/10.1007/BFb0043220

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