ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About Asymptothic Versions of the One-impulse Control in the Linear System: Attraction Sets in the Space of Trajectories


A. G. Chentsov

Inststute of Mathematics and Mechanics of Ural Department of RAN
S.Kovalevskoi st., 16, 620219 Ekaterinburg, Russia

A. V. Lysenko

Faculty of mathematics and mechanics
Ural State University
Lenina st., 51, 620083 Ekaterinburg, Russia


An asymptotic variant of the problem of construction of the bandle of trajectories for linear system in the class of one-impulse controls with limited power resource is considered. Discontinuous dependences for coefficients at the controls is allowed. The attraction set (AS) in the space of trajectories with the topology of pointwise convergence is constructed. The structure of the AS is determined from the solution of generalized problem in the class of finitelly-additive measures. The representation of the AS is obtained for the controls which correspond to application of "narrow" impulses with the total consumption of the power resource.

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