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Approximate Synthesis of Distributed Bounded Control for a Parabolic Problem with Rapidly Oscillating Coefficients

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Ukrainian Mathematical Journal Aims and scope

We study the problem of finding the optimal control in the form of feedback (synthesis) for a linear-quadratic problem in the form of a parabolic equation with rapidly oscillating coefficients and distributed control on the right-hand side (whose Fourier coefficients obey certain restrictions in the form of inequalities) and a quadratic quality criterion. We deduce the exact formula of synthesis and justify its approximate form corresponding to the replacement of rapidly oscillating coefficients by their averaged values.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv, Ukraine

    O. V. Kapustyan & A. V. Rusina

Authors
  1. O. V. Kapustyan
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  2. A. V. Rusina
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 3, pp. 355–365, March, 2015.

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Kapustyan, O.V., Rusina, A.V. Approximate Synthesis of Distributed Bounded Control for a Parabolic Problem with Rapidly Oscillating Coefficients. Ukr Math J 67, 408–420 (2015). https://doi.org/10.1007/s11253-015-1089-x

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  • DOI: https://doi.org/10.1007/s11253-015-1089-x

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