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Computational Mathematics and Modeling

, Volume 18, Issue 4, pp 332–343 | Cite as

Optimal boundary control of vibrations at one endpoint of a string when the second endpoint is free

  • V. A. Il’in
  • E. I. Moiseev
Article
  • 23 Downloads

Abstract

The generalized solution u(x, t) of the wave equation u tt (x, t) − u xx (x, t) = 0 admitting the existence of finite energy at every time instant t is used to find among all W 2 1 [0,T]-functions with a long time interval T the optimal boundary control for a string with a free endpoint that takes the vibration process from a given arbitrary state to a given final state.

Keywords

Wave Equation Generalize Solution Boundary Control Boundary Energy Arbitrary State 
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

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    V. A. Il’in, “Boundary control of the vibration process at two endpoints in terms of the finite-energy generalized solution of the wave equation,” Different. Uravn., 36,No. 11, 1513–1528 (2000).Google Scholar
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    V. A. Il’in, “Boundary control of the vibration process at one endpoint when the second endpoint is fixed in terms of the finite-energy generalized solution of the wave equation,” Different. Uravn., 36,No. 12, 1670–186 (2000).Google Scholar
  3. 3.
    P. A. Revo and G. D. Chabakauri, “Boundary control of the vibration process at one endpoint when the second endpoint is free in terms of the finite-energy generalized solution of the wave equation,” Different. Uravn., 37,No. 8, 1082–1095 (2001).MathSciNetGoogle Scholar
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    G. D. Chabakauri, Optimal Boundary Control of the Vibration Process [in Russian], Author’s Abstract of the Candidate Degree Thesis (Physics and Mathematics), Moscow (2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • V. A. Il’in
  • E. I. Moiseev

There are no affiliations available

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