Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2009-4pp.411-420

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S.A. Ganebnyi, S.S. Kumkov, and V.S. Patsko, "Extremal aiming in problems with an unknown level of dynamic disturbance," J. Appl. Math. Mech. 73 (4), 411-420 (2009)
Year 2009 Volume 73 Issue 4 Pages 411-420
Title Extremal aiming in problems with an unknown level of dynamic disturbance
Author(s) S.A. Ganebnyi (Ekaterinburg, Russia)
S.S. Kumkov (Ekaterinburg, Russia)
V.S. Patsko (Ekaterinburg, Russia,
Abstract The method of extremal aiming, well-known in the theory of differential games, is applied to problems in which the level of dynamic disturbance is not stipulated in advance. Problems with linear dynamics, a fixed termination time and a geometric constraint on the effective control are considered. The aim of the control is to bring the system into a specified terminal set at the instant of termination. A feedback control method is proposed which ensures successful completion if the disturbance does not exceed a certain critical level. Here, "weak" disturbance is countered by a "weak" effective control. A guarantee theorem is formulated and proved. An illustrative example is considered.
Received 23 December 2008
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