Approximate Synthesis of Distributed Bounded Control for a Parabolic Problem with Rapidly Oscillating Coefficients
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...
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| Date: | 2015 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2015
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1988 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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