Skip to main content
SpringerLink
Log in
Book cover

System Modelling and Optimization pp 535–541Cite as

Time optimal boundary controllability of a viscoelastic beam

  • Conference paper
  • First Online:

  • 116 Accesses

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 84))

Abstract

It is shown that the vibrations of a viscoelastic beam can be steered to rest in minimal time using a L2(O,T)-boundary control realizing a prescribed norm-bound.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N.N. Ahmed, Finite-time null controllability for a class of linear evolution equations on a Banach space with control constraints, JOTA, 47/2, 129–158, (1985).

    Google Scholar 

  2. A.V. Balakrishnan, Applied functional analysis, Springer-Verlag 1976.

    Google Scholar 

  3. C.M. Dafermos, Contraction semigroup and trend to equilibrium in continuum mechanics, in Applications of Functional Analysis to Problems in Mechanics (Springer, 1976).

    Google Scholar 

  4. G.W. Desch and R.C. Grimmer, Initial boundary value problems for integro-differential equations, J. of Int. Eq., to appear.

    Google Scholar 

  5. R.F. Curtain, Finite dimensional compensators for some hyperbolic systems with boundary control; Control theory for distributed parameter systems and applications, Lecture Notes in Control and Information Sciences 54, Springer (1983), 77–92.

    Google Scholar 

  6. S.I. Gaiduk, Some problems related to the theory of the action of a transverse impulse on a rod, Differential Equations, 13/II, 854–861 (1977).

    Google Scholar 

  7. J.S. Gibson, An analysis of optimal modal regulation: convergence and stability; SIAM J. Control and Opt. 19/5, 686–707 (1981).

    Google Scholar 

  8. I. Lasiecka and R. Triggiani, A cosine operator approach to modelling L2(O,T,L2(τ))-boundary hyperbolic equations, J. Appl. Math. & Opt., 7, 35–93 (1981).

    Google Scholar 

  9. G. Leugering, Boundary controllability of a viscoelastic beam, Applicable Analysis, to appear.

    Google Scholar 

  10. A. Marzollo, Controllability and optimization, CISM Lecture No. 17, Udine 1969, Springer Verlag (1972).

    Google Scholar 

  11. K. Narukawa, Exact and admissible controllability of viscoelastic systems with boundary controls, Preprint.

    Google Scholar 

  12. K. Narukawa, Admissible null controllability and optimal time control, Hiroshima Math. J., 11/3, 533–551 (1983).

    Google Scholar 

  13. Y. Sakawa, Feedback control of second order evolution equations with damping; SIAM J. Control and Opt. 22/3, 343–361 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik der Technischen Hochschule Darmstadt, Schlossgartenstr. 7, 6100, Darmstadt, West Germany

    G. Leugering

Authors
  1. G. Leugering
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

A. Prékopa J. Szelezsáan B. Strazicky

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Leugering, G. (1986). Time optimal boundary controllability of a viscoelastic beam. In: Prékopa, A., Szelezsáan, J., Strazicky, B. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043877

Download citation

  • DOI: https://doi.org/10.1007/BFb0043877

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16854-6

  • Online ISBN: 978-3-540-47138-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation