Geodesic
Point control of a differential-difference system with distributed parameters on the graph
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 3, pp. 277-286

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

The article considers the problem of point control of the differential-difference equation with distributed parameters on the graph in the class of summable functions. The differential-difference system is closely related to the evolutionary differential system and moreover the properties of the differential system are preserved. This connection is established by the universal method of semi-discretization in a time variable for a differential system, which provides an effective tool in order to find conditions for unique solvability and continuity on the initial data for the differential-difference system. For this differential-difference system, a special case of the optimal control problem is studied: the problem of point control action on the controlled differential-difference system is considered by the control, concentrated at all internal nodes of the graph. At the same time, the restrictive set of permissible controls is set by the means of conditions depending on the nature of the applied tasks. In this case, the controls are concentrated at the end points of the edges adjacent to each inner node of the graph. This is a characteristic feature of the study presented, quite often used in practice when building a mechanism for managing the processes of transportation of different kinds of masses over network media. The study essentially uses the conjugate state of the system and the conjugate system for a differential-difference system — obtained ratios that determine optimal point control. The obtained results underlie the analysis of optimal control problems for differential systems with distributed parameters on the graph, which have interesting analogies with multi-phase problems of multidimensional hydrodynamics.
Keywords: differential-difference system, conjugate system, oriented graph, optimal point control. 
@article{VSPUI_2021_17_3_a4,
     author = {V. V. Provotorov and S. M. Sergeev and V. N. Hoang},
     title = {Point control of a differential-difference system with distributed parameters on the graph},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {277--286},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_3_a4/}
}
TY  - JOUR
AU  - V. V. Provotorov
AU  - S. M. Sergeev
AU  - V. N. Hoang
TI  - Point control of a differential-difference system with distributed parameters on the graph
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 277
EP  - 286
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2021_17_3_a4/
LA  - en
ID  - VSPUI_2021_17_3_a4
ER  - 
%0 Journal Article
%A V. V. Provotorov
%A S. M. Sergeev
%A V. N. Hoang
%T Point control of a differential-difference system with distributed parameters on the graph
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2021
%P 277-286
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSPUI_2021_17_3_a4/
%G en
%F VSPUI_2021_17_3_a4
V. V. Provotorov; S. M. Sergeev; V. N. Hoang. Point control of a differential-difference system with distributed parameters on the graph. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 3, pp. 277-286. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_3_a4/