Geodesic
Evasion of the meeting in a~cone in third order differential game
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 3, pp. 93-104.

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

It is considered a problem of conflict interaction of one evader from a group of pursuers with equal dynamic capabilities of all players. The motion of each player is defined by third order differential equation. Initial conditions are set. It is proved that if number of pursuers is less than space dimension and the initial position, velocity and acceleration of the evader are inside of the given cone, then runaway occurs.
Keywords: differential game, evasion from many pursuers in a cone, state constraints. 
@article{MGTA_2014_6_3_a4,
     author = {Lyubov S. Chirkova},
     title = {Evasion of the meeting in a~cone in third order differential game},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {93--104},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a4/}
}
TY  - JOUR
AU  - Lyubov S. Chirkova
TI  - Evasion of the meeting in a~cone in third order differential game
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2014
SP  - 93
EP  - 104
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a4/
LA  - ru
ID  - MGTA_2014_6_3_a4
ER  - 
%0 Journal Article
%A Lyubov S. Chirkova
%T Evasion of the meeting in a~cone in third order differential game
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2014
%P 93-104
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a4/
%G ru
%F MGTA_2014_6_3_a4
Lyubov S. Chirkova. Evasion of the meeting in a~cone in third order differential game. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 3, pp. 93-104. http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a4/

[1] Bannikov A. S., 3–10, Vestnik Udmurtskogo universiteta. Matematika, no. 1, 2010

[2] Bannikov A. S., “Nekotorye nestatsionarnye zadachi gruppovogo presledovaniya”, Izvestiya IMI UdGU, 2013, no. 1(41), 3–46 | Zbl

[3] Blagodatskikh A. I., Petrov N. N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov, Izhevsk, 2009, 266 pp. | MR

[4] Zak V. L., “Zadacha ukloneniya ot mnogikh presledovatelei, upravlyaemykh po uskoreniyu”, Izvestiya AN SSSR. Tekhnicheskaya kibernetika, 1981, no. 2, 51–71 | MR

[5] Petrov N. N., “K nestatsionaroi zadache gruppovogo presledovaniya s fazovymi ogranicheniyami”, Matematicheskaya teoriya igr i ee prilozheniya, 2:4 (2010), 74–83 | Zbl

[6] Petrov N. N., Schelchkov K. A., “K zadache Chernousko”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2012, no. 4, 62–67

[7] Prokopovich P. V., Chikrii A. A., “Odna differentsialnaya igra ubeganiya”, DAN USSR. Seriya A, 1989, no. 1, 71–74 | MR | Zbl

[8] Pshenichnyi B. N., “Prostoe presledovanie neskolkimi ob'ektami”, Kibernetika, 1976, no. 3, 145–146

[9] Sakharov D. V., “O dvukh differentsialnykh igrakh prostogo gruppovogo presledovaniya”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2012, no. 1, 50–59

[10] Chernousko F. L., “Odna zadacha ukloneniya ot mnogikh presledovatelei”, PMM, 40:1 (1976), 14–24 | Zbl

[11] Chikrii A. A., Prokopovich P. V., “Zadacha ubeganiya ot gruppy dlya odnotipnykh inertsionnykh ob'ektov”, Differents. uravneniya, 30:6 (1994), 998–1004 | MR

[12] Chirkova L. S., “Uklonenie ot gruppy inertsionnykh ob'ektov v konuse”, Izvestiya IMI UdGU, 2000, no. 2(19), 59–72

[13] Chirkova L. S., “Uklonenie ot gruppy inertsionnykh ob'ektov”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2007, no. 3, 45–53 | MR | Zbl