Geodesic
Collective Pursuit with Integral Constraints on the~Controls of~Players
Matematičeskie trudy, Tome 6 (2003) no. 2, pp. 66-79

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Under consideration is a linear differential game of several persons with integral constraints on the controls of the players. Pursuit terminates if a solution to at least one of the equations describing the differential game hits the origin at some instant of time. We establish a necessary and sufficient condition of terminating pursuit from all points of the space in the case of a single pursuer and a sufficient condition in the case of many pursuers. 
@article{MT_2003_6_2_a2,
     author = {G. I. Ibragimov},
     title = {Collective {Pursuit} with {Integral} {Constraints} on {the~Controls} {of~Players}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {66--79},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2003_6_2_a2/}
}
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G. I. Ibragimov. Collective Pursuit with Integral Constraints on the~Controls of~Players. Matematičeskie trudy, Tome 6 (2003) no. 2, pp. 66-79. http://geodesic.mathdoc.fr/item/MT_2003_6_2_a2/