Abstract
For a string vibration process described by an inhomogeneous wave equation, we consider the problem of boundary control at one end of the string with the other end being fixed. For any time interval T > 2l, where l is the string length, we find a function u(0, t) = µ(t) bringing the vibration system from a given initial state into a given terminal state and minimizing the boundary energy integral.
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Original Russian Text © M.F. Abdukarimov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 5, pp. 680–691.
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Abdukarimov, M.F. Optimal boundary control of forced vibrations by the displacement at one end of the string with the other end fixed. Diff Equat 50, 677–688 (2014). https://doi.org/10.1134/S0012266114050103
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DOI: https://doi.org/10.1134/S0012266114050103