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Russian Academy of Sciences		 Founded
in January 1936
(Translated from 1958)
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Issues > Archive of Issues > 2009-4 > pp.403-410

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S.A. Reshmin, "Bifurcation in a time-optimal problem for a second-order non-linear system," J. Appl. Math. Mech. 73 (4), 403-410 (2009)
Year 2009 Volume 73 Issue 4 Pages 403-410
Title Bifurcation in a time-optimal problem for a second-order non-linear system
Author(s) S.A. Reshmin (Moscow, Russia, reshmin@ipmnet.ru)
Abstract A time-optimal problem for a second-order non-linear system with one degree of freedom is considered. The system describes the dynamics of an inertial object under the action of a control force of limited modulus which appears linearly and a perturbing force which is periodic in coordinate. The terminal set represents points on the abscissa of the phase plane, and the distance between two neighbouring points is equal to the period of the perturbing force. An estimate is obtained for the amplitude of the control for which the control has the simplest structure: the number of switchings is not greater than one.
Received 08 December 2008
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