Abstract
A determination problem of external, surface-distributed controlling load that transfers a circular elastic plate from one prescribed initial state as close as possible to another prescribed finite state in a fixed period of time is considered. The problem is posed as a minimization problem of terminal quadratic quality functional on solutions to a linear equation that describes plate vibrations with controls in the right-hand side of the equation. Controls depend only on time, and their distribution on the plate surface is fixed. To solve this control problem, a dual regularized method is applied. A description of the solution algorithm is given, estimates of a rate of functional convergence and conditions of control convergence are obtained.
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Original Russian Text © A.Z. Ishmukhametov, R. Makhrous, 2007, published in Avtomatika i Telemekhanika, 2007, No. 2, pp. 162–170.
This work was supported by the Russian Foundation for Basic Research, project no. 04-01-00619.
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Ishmukhametov, A.Z., Makhrous, R. A dual regularized method in a control problem of plate vibrations. Autom Remote Control 68, 361–368 (2007). https://doi.org/10.1134/S0005117907020166
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DOI: https://doi.org/10.1134/S0005117907020166