Geodesic
Simple pursuit problem with phase restrictions of two coordinated evaders on time scales
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 14 (2022) no. 4, pp. 81-95.

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

In a finite-dimensional Euclidean space, the problem of a simple pursuit by a group of pursuers of two evaders is considered on a given time scale. It is assumed that all evaders use the same control and do not leave the convex polyhedral set. The pursuers use counter-strategies based on information about the initial positions and control history of the evaders. The set of admissible controls for each of the participants is a unit ball centered at zero, the target sets are the origin. The goal of the pursuers' group is the capture by two pursuers of at least one evader or the capture of two evaders. In terms of the initial positions and game parameters a sufficient capture condition has been obtained. The study uses the method of resolving functions as a basic one, which allows to obtain sufficient conditions for the solvability of the approach problem in some guaranteed time.
Keywords: differential game, group pursuit, evader, pursuer
Mots-clés : time scale. 
@article{MGTA_2022_14_4_a4,
     author = {Nikolai N. Petrov and Elena S. Mozhegova},
     title = {Simple pursuit problem with phase restrictions of two coordinated evaders on time scales},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {81--95},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2022_14_4_a4/}
}
TY  - JOUR
AU  - Nikolai N. Petrov
AU  - Elena S. Mozhegova
TI  - Simple pursuit problem with phase restrictions of two coordinated evaders on time scales
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2022
SP  - 81
EP  - 95
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2022_14_4_a4/
LA  - ru
ID  - MGTA_2022_14_4_a4
ER  - 
%0 Journal Article
%A Nikolai N. Petrov
%A Elena S. Mozhegova
%T Simple pursuit problem with phase restrictions of two coordinated evaders on time scales
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2022
%P 81-95
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2022_14_4_a4/
%G ru
%F MGTA_2022_14_4_a4
Nikolai N. Petrov; Elena S. Mozhegova. Simple pursuit problem with phase restrictions of two coordinated evaders on time scales. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 14 (2022) no. 4, pp. 81-95. http://geodesic.mathdoc.fr/item/MGTA_2022_14_4_a4/

[1] Blagodatskikh A.I., Petrov N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Izd. Udmurt. un-ta, Izhevsk, 2009

[2] Grigorenko N.L., Matematicheskie metody upravleniya neskolkimi dinamicheskimi protsessami, Izd-vo MGU, M., 1990

[3] Krasovskii N.N., Subbotin A.I., Pozitsionnye differentsialnye igry, Nauka, M., 1974

[4] Petrov N.N., “Zadacha prostogo gruppovogo presledovaniya s fazovymi ogranicheniyami vo vremennykh shkalakh”, Vestnik Udmurtskogo un-ta. Matematika. Mekhanika. Kompyuternye nauki, 30:2 (2020), 249–258

[5] Petrov N.N., “Ob odnoi zadache presledovaniya gruppy ubegayuschikh vo vremennykh shkalakh”, Trudy IMM UrO RAN, 27, no. 3, 2021, 163–171

[6] Petrov N.N., “Ob upravlyaemosti avtonomnykh sistem”, Differents. uravneniya, 4:4 (1968), 606–617

[7] Chikrii A.A., Konfliktno upravlyamye protsessy, Nauk. dumka, Kiev, 1992

[8] Aulbach B., Hilger S., “Linear dynamic processes with inhomogeneous time scale”, Nonlinear Dynamics and Quantum Dynamical Systems, 59 (1990), 9–20

[9] Benchohra M., Henderson J., Ntouyas S., Impulsive Differential Equations and Inclusions, Hindawi Publishing, New York, 2006

[10] Bohner M., Peterson A., Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003

[11] Cabada A., Vivero D. R., “Expression of the Lebesgue $\Delta$-integral on time scales as a usual Lebesgue integral; application to the calculus of $\Delta$-antiderivatives”, Mathematical and Computer Modelling, 43:1-2 (2006), 194–207

[12] Guseinov G.S., “Integration on time scales”, Journal of Math. Anal. Appl., 285:1 (2003), 107–127

[13] Hilger S., “Analysis on measure chains - a unified approach to continuous and discrete calculus”, Results in Mathematics, 18 (1990), 18–56

[14] Martins N., Torres D., “Necessary conditions for linear noncooperative $N$-player delta differential games on time scales”, Discussiones Mathematicae, Differential Inclusions, Control and Optimization, 31:1 (2011), 23–37

[15] Petrov N.N., “Multiple Capture of a Given Number of Evaders in the Problem of Simple Pursuit with Phase Restrictions on Timescales”, Dyn. Games Appl., 12:2 (2022), 632–642