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On tracking solutions of parabolic equations

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Abstract

We consider a control problem for a parabolic equation. It consists in constructing an algorithm for finding a feedback control such that a solution of a given equation should track a solution of another equation generated by an unknown right-hand side. We propose two noise-resistant solution algorithms for the indicated problem. They are based on the method of extremal shift well-known in the guaranteed control theory. The first algorithm is applicable in the case of “continuous” measurements of phase states, whereas the second one implies discrete measurements.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia

    V. I. Maksimov

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  1. V. I. Maksimov
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Correspondence to V. I. Maksimov.

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Original Russian Text © V.I. Maksimov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 1, pp. 40–48.

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Maksimov, V.I. On tracking solutions of parabolic equations. Russ Math. 56, 35–42 (2012). https://doi.org/10.3103/S1066369X12010057

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  • DOI: https://doi.org/10.3103/S1066369X12010057

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