Geodesic
On a control problem for a discrete system
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 311-318 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article proposes one of the approaches for solving the control problem of a linear discrete system. A conflict-controlled process is considered whose duration is given. It is required that at the end of the control process the phase point is contained in a given set. Rules governing the control of a discrete system contain discrimination for the second player. The case is considered when the control vector and a given set are polyhedra given by a system of linear inequalities. It is assumed that for polyhedra a certain property of linearity is satisfied, which makes it possible to obtain the solution of the problem explicitly. The operator of operator absorption is introduced into the consideration in the paper. With the help of this operator, conditions are written for a set of initial positions under which the required inclusion is guaranteed at the time of the end of the control process. These conditions are written in the form of a system of inequalities. The practical part of the work shows the application of the obtained results to economic systems. The solution of the problem of inventory management is given.
Keywords: discrete system, multi-step control problem, polyhedral control set, inventory management problem. 
@article{CHFMJ_2018_3_3_a3,
     author = {S. A. Nikitina and A. S. Scorynin and V. I. Ukhobotov},
     title = {On a control problem for a discrete system},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {311--318},
     year = {2018},
     volume = {3},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a3/}
}
TY  - JOUR
AU  - S. A. Nikitina
AU  - A. S. Scorynin
AU  - V. I. Ukhobotov
TI  - On a control problem for a discrete system
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2018
SP  - 311
EP  - 318
VL  - 3
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a3/
LA  - ru
ID  - CHFMJ_2018_3_3_a3
ER  - 
%0 Journal Article
%A S. A. Nikitina
%A A. S. Scorynin
%A V. I. Ukhobotov
%T On a control problem for a discrete system
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2018
%P 311-318
%V 3
%N 3
%U http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a3/
%G ru
%F CHFMJ_2018_3_3_a3
S. A. Nikitina; A. S. Scorynin; V. I. Ukhobotov. On a control problem for a discrete system. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 311-318. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a3/

[1] Uhobotov V.I., Nikitina S.A., “Stable bridge for a class of differential games”, Bulletin of Chelyabinsk State University, 2003, no. 1 (7), 99–107 (In Russ.) | MR

[2] Uhobotov V.I., Nikitina S.A., “Construction of guaranteed control in quasilinear systems”, Proceedings of the Institute of Mathematics and Mechanics. Dynamic Systems and Control Problems, 1:5 (2005), 201–211 (In Russ.)

[3] Uhobotov V.I., Stabulit I.S., “Dynamic control problem in the presence of interference and with a given set of correction moments”, The Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 28:1 (2018), 74–81 (In Russ.) | MR | Zbl

[4] Propoy A.I., Elements of the theory of optimal discrete processes, Nauka Publ., Moscow, 1973, 256 pp. (In Russ.)

[5] Pshenichny B.N., Convex analysis and extremal problems, Mir Publ., Moscow, 1980, 319 pp. (In Russ.) | MR

[6] Uhobotov V.I., “To the construction of stable bridges”, Applied Mathematics and Mechanics, 44:5 (1980), 934–938 (In Russ.) | MR

[7] Pontryagin L.S., “Linear differential games. II”, Reports of the USSR Academy of Sciences, 175:4 (1967), 764–766. (In Russ.) | Zbl

[8] Uhobotov V.I., Nikitina S.A., “Calculation of the game price function for a class of decompositional differential games”, News of the Institute of Mathematics and Informatics of the Udmurt State University, 2006, no. 3 (37), 153–154 (In Russ.)