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NONLINEAR WAVE EQUATIONS AND BOUNDARY CONTROL USING VISCO ELASTIC DAMPERS

  • Stephen P. Banks
  • Metin U. Salamcı
Conference paper
  • 1.3k Downloads
Part of the Springer Proceedings in Physics book series (SPPHY, volume 111)

Abstract

In this paper we shall study the boundary control and stabilization of nonlinear wave systems which are controlled by viscoelastic dampers on the boundary. This requires the use of fractional derivatives and a recent ‘iteration’ technique for converting nonlinear problems into a sequence of time-varying linear ones. We shall use the theory of evolution operators on Hilbert space and obtain an abstract setting for the problem.

Keywords

Fractional Derivative Nonlinear Wave Evolution Operator Boundary Control Nonlinear Wave Equation 
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References

  1. Banks S. P. (2001) Exact boundary control lability and optimal control for a generalised Korteweg-de Vries equation, J. Nonlinear Anal- Apps and Methods. 47, 5537–5546.CrossRefGoogle Scholar
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  3. Krall A. (1989) Asymptotic Stability of the Euler-Bernoulli Beam with Boundary Control, J. Math. Anal. App. 137, 288–295.CrossRefMathSciNetGoogle Scholar
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  5. Podlubny I. (1999) Fractional Differential Equations, Maths, in Sci. and Eng., Vol 198, Academic Press.Google Scholar
  6. Rodriguez M. T., Banks S. (2003) Linear Approximations to Nonlinear Dynamical Systems with Applications to Stability and Spectral Theory, IMA J. Math. Cont. 20, 89–103.CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Stephen P. Banks
    • 1
  • Metin U. Salamcı
    • 2
  1. 1.Automatic Control and Systems Eng.The University of SheffieldSheffieldUK
  2. 2.Mechanical Engineering DepartmentGazi UniversityAnkaraTurkey

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