Geodesic
Resolution of linear-quadratic problems in a discrete-continuous format with external actions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 45 (2023), pp. 24-36

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

Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations.
Keywords: linear-quadratic problems, discrete actions to system and functional, reduction to convex problems. 
@article{IIGUM_2023_45_a1,
     author = {Vladimir A. Srochko and Vladimir G. Antonik},
     title = {Resolution of linear-quadratic problems in a discrete-continuous format with external actions},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {24--36},
     publisher = {mathdoc},
     volume = {45},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a1/}
}
TY  - JOUR
AU  - Vladimir A. Srochko
AU  - Vladimir G. Antonik
TI  - Resolution of linear-quadratic problems in a discrete-continuous format with external actions
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2023
SP  - 24
EP  - 36
VL  - 45
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a1/
LA  - ru
ID  - IIGUM_2023_45_a1
ER  - 
%0 Journal Article
%A Vladimir A. Srochko
%A Vladimir G. Antonik
%T Resolution of linear-quadratic problems in a discrete-continuous format with external actions
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2023
%P 24-36
%V 45
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a1/
%G ru
%F IIGUM_2023_45_a1
Vladimir A. Srochko; Vladimir G. Antonik. Resolution of linear-quadratic problems in a discrete-continuous format with external actions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 45 (2023), pp. 24-36. http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a1/