Approximate Homogenized Synthesis for Distributed Optimal Control Problem with Superposition Type Cost Functional

  • Olena A. Kapustian Taras Shevchenko National University of Kyiv, Ukraine
  • Valentyn V. Sobchuk Lesya Ukrainka Eastern European National University, Lutsk
DOI: https://doi.org/10.19139/soic.v6i2.305
Keywords: the optimal control problem, approximate synthesis, parabolic equation, rapidly oscillating coefficients, homogenization

Abstract

In this paper, we consider the optimal control problem in the feedback form (synthesis) for a parabolic equation with rapidly oscillating coefficients and not-decomposable quadratic cost functional with superposition type operator. In general, to find the exact formula of optimal synthesis is not possible for such a problem because the Fourier method can’t be directly applied. But the transition to the homogenized parameters greatly simplifies the structure of the problem. Assuming that the problem with the homogenized coefficients already admits optimal synthesis form, we ground approximate optimal control in the feedback form for the initial problem. We give an example of superposition operator for specific conditions in this paper.

Author Biographies

Olena A. Kapustian, Taras Shevchenko National University of Kyiv, Ukraine
Faculty of Computer Science and Cybernetics,Deputy Dean
Valentyn V. Sobchuk, Lesya Ukrainka Eastern European National University, Lutsk
Faculty of Information Systems, Physics and Mathematics,Associate Professor

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Published
2018-06-24
How to Cite
Kapustian, O. A., & Sobchuk, V. V. (2018). Approximate Homogenized Synthesis for Distributed Optimal Control Problem with Superposition Type Cost Functional. Statistics, Optimization & Information Computing, 6(2), 233-239. https://doi.org/10.19139/soic.v6i2.305
Issue
Vol 6 No 2 (2018)
Section
Research Articles
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