This article is cited in 13 papers

On tracking solutions of parabolic equations

V. I. Maksimov

Department of Differential Equations, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

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 extremal shift method well-known in the guaranteed control theory. The first algorithm is applicable in the case of “continuous” measuring of phase states, whereas the second one implies discrete measuring.

Keywords: systems with distributed parameters, control.

UDC: 519.633

Received: 08.02.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:1, 35–42

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