On two problems of pursuit of a group of evaders in differential games with fractional derivatives
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 1, pp. 65-79
Voir la notice de l'article provenant de la source Math-Net.Ru
In a finite-dimensional Euclidean space, the problem of pursuit of a group of evaders by a group of pursuers is considered, described by a system of the form
\begin{gather*}
D^{(\alpha)}x_i = a_i x_i + u_i, \ u_i \in U_i, \quad D^{(\alpha)}y_j = b_jy_j + v, \ v\in V,
\end{gather*}
where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha$ of the function $f$. The sets of admissible controls $U_i, V$ are convex compacts, $a_i, b_j$ are real numbers. The terminal sets are convex compacts. Sufficient conditions for the solvability of the pursuit problems are obtained. In the study, the method of resolving functions is used as the basic one. It is shown that such a conflict situation with equal opportunities for all participants is possible, in which one pursuer catches all the evaders.
Keywords:
differential game, group pursuit, pursuer, evader, fractional derivative
@article{VUU_2024_34_1_a4,
author = {A. I. Machtakova and N. N. Petrov},
title = {On two problems of pursuit of a group of evaders in differential games with fractional derivatives},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {65--79},
publisher = {mathdoc},
volume = {34},
number = {1},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a4/}
}
TY - JOUR AU - A. I. Machtakova AU - N. N. Petrov TI - On two problems of pursuit of a group of evaders in differential games with fractional derivatives JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2024 SP - 65 EP - 79 VL - 34 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a4/ LA - ru ID - VUU_2024_34_1_a4 ER -
%0 Journal Article %A A. I. Machtakova %A N. N. Petrov %T On two problems of pursuit of a group of evaders in differential games with fractional derivatives %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2024 %P 65-79 %V 34 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a4/ %G ru %F VUU_2024_34_1_a4
A. I. Machtakova; N. N. Petrov. On two problems of pursuit of a group of evaders in differential games with fractional derivatives. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 1, pp. 65-79. http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a4/