Geodesic
The closure of the sheaf of trajectories of a~linear control system with integral constraints
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2009), pp. 59-68

Voir la notice de l'article provenant de la source Math-Net.Ru

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 the 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.
Keywords: control system, generalized problem, finite additive measures. 
@article{IVM_2009_12_a6,
     author = {S. I. Tarasova},
     title = {The closure of the sheaf of trajectories of a~linear control system with integral constraints},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {59--68},
     publisher = {mathdoc},
     number = {12},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_12_a6/}
}
TY  - JOUR
AU  - S. I. Tarasova
TI  - The closure of the sheaf of trajectories of a~linear control system with integral constraints
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 59
EP  - 68
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_12_a6/
LA  - ru
ID  - IVM_2009_12_a6
ER  - 
%0 Journal Article
%A S. I. Tarasova
%T The closure of the sheaf of trajectories of a~linear control system with integral constraints
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 59-68
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_12_a6/
%G ru
%F IVM_2009_12_a6
S. I. Tarasova. The closure of the sheaf of trajectories of a~linear control system with integral constraints. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2009), pp. 59-68. http://geodesic.mathdoc.fr/item/IVM_2009_12_a6/