Fractional order differential pursuit games with nonlinear controls
Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 132, pp. 401-409
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The article is devoted to the problems of extending the results and methods of the theory of differential games and optimal control to systems of fractional order. The research is motivated by numerous applications of fractional calculus in control problems of industrial facilities, chemical and biochemical plants, etc. The article considers the problem of pursuit in games represented by nonlinear differential equations of arbitrary fractional order in the sense of Caputo. To study this pursuit problem, we use an approach similar to the method of L. S. Pontryagin, developed for linear differential games of integer orders. In this paper, new sufficient conditions are obtained for solving the pursuit problem in the class of games under study. It has been proven that if these conditions are met, the game can be completed within a certain limited period of time. When solving the pursuit problem, we also used the representation of the solution to a differential equation in terms of generalized matrix functions.
Keywords:
fractional differential equation, escaping player, pursuing player, terminal set, derivative in the sense of Caputo.
@article{VTAMU_2020_25_132_a4,
author = {M. Sh. Mamatov and Kh. N. Alimov},
title = {Fractional order differential pursuit games with nonlinear controls},
journal = {Vestnik rossijskih universitetov. Matematika},
pages = {401--409},
publisher = {mathdoc},
volume = {25},
number = {132},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTAMU_2020_25_132_a4/}
}
TY - JOUR AU - M. Sh. Mamatov AU - Kh. N. Alimov TI - Fractional order differential pursuit games with nonlinear controls JO - Vestnik rossijskih universitetov. Matematika PY - 2020 SP - 401 EP - 409 VL - 25 IS - 132 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VTAMU_2020_25_132_a4/ LA - ru ID - VTAMU_2020_25_132_a4 ER -
%0 Journal Article %A M. Sh. Mamatov %A Kh. N. Alimov %T Fractional order differential pursuit games with nonlinear controls %J Vestnik rossijskih universitetov. Matematika %D 2020 %P 401-409 %V 25 %N 132 %I mathdoc %U http://geodesic.mathdoc.fr/item/VTAMU_2020_25_132_a4/ %G ru %F VTAMU_2020_25_132_a4
M. Sh. Mamatov; Kh. N. Alimov. Fractional order differential pursuit games with nonlinear controls. Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 132, pp. 401-409. http://geodesic.mathdoc.fr/item/VTAMU_2020_25_132_a4/