Geodesic
Discrete dynamic systems with interference and their applications to the solution of the problem of reserve control
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 10 (2021) no. 2, pp. 5-19

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Two models of discrete dynamic controlled systems with noise are considered. In one of them a discrete control problem is presented, in which the control vectogram linearly depends on the given sets. In the second problem, it is assumed that the control and noise vectograms are of the same type. In both cases, the purpose of the choice of control is that at the moment of the end of the control process the phase point is contained in the given set. When constructing the control, it is assumed that at each discrete moment of time, information about the implementation of the interference arrives. The operator of programmed absorption is written down, with the help of which conditions are formulated for the set of initial positions under which the fulfillment of the required inclusion at a given moment of time is guaranteed. In the practical part of the work, the application of the results obtained is shown by the example of solving the problem of managing the inventory of goods in the warehouse. Replenishment of goods occurs due to its production, and the amount of shipment of goods is determined by demand. It is assumed that only the set of its values is known about the amount of demand for a product. The goal of control is that at a given moment in time, the quantity of goods satisfies certain restrictions. A lot of initial stocks of goods have been obtained, for which it is possible to fulfill the set goal for any realization of demand.
Keywords: discrete system, reserve control problem, vectograms, linearly dependent on given sets, the same type of control problem. 
@article{VYURV_2021_10_2_a0,
     author = {S. A. Nikitina and V. I. Ukhobotov},
     title = {Discrete dynamic systems with interference and their applications to the solution of the problem of reserve control},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {5--19},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2021_10_2_a0/}
}
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S. A. Nikitina; V. I. Ukhobotov. Discrete dynamic systems with interference and their applications to the solution of the problem of reserve control. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 10 (2021) no. 2, pp. 5-19. http://geodesic.mathdoc.fr/item/VYURV_2021_10_2_a0/