The Closure of the Sheaf of Trajectories of a Linear Control System with Integral Constraints

被引:0
作者
Tarasova, S. I. [1 ]
机构
[1] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ul S Kovalevskoi 16, Ekaterinburg 620219, Russia
基金
俄罗斯基础研究基金会;
关键词
control system; generalized problem; finite additive measures;
D O I
10.3103/S1066369X0912007X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider a linear system with discontinuous coefficients controlled by a parameter under an integral constraint imposed on the control resource. It is well known that in such problems the closure of the sheaf of trajectories that correspond to ordinary controls (piecewise constant or measurable functions) coincides with the sheaf of trajectories in a generalized problem, where for generalized controls one uses finite additive measures of bounded variation. Therewith the closure is defined in the topology of pointwise convergence, because the limit elements (the generalized trajectories) may be discontinuous functions. In this paper we prove that any generalized trajectory can be approximated by a sequence of ordinary solutions to the initial system. We propose a concrete technique for constructing such sequences.
引用
收藏
页码:50 / 58
页数:9
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