Geodesic
Some non-stationary problems of group pursuit
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 41 (2013) no. 1, pp. 3-46

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We consider non-stationary problems of conflict interaction of one or several evaders with a group of pursuers at the same dynamic and inertial opportunities of all players. We obtain sufficient conditions for the solvability of the local evasion problem in a linear non-stationary problem and the solvability of the global problem of evasion of group of evaders from a group of pursuers in the non-stationary problem of group pursuit with a diagonal matrix. We obtain two-sided estimate the minimum number of evaders sufficient for the solvability of the avoidance from any initial position for a given number of pursuers in games with a diagonal matrix. For non-stationary problem of simple pursuit with phase constraints, we propose a positional control procedure with a guide that guarantees capture at least one of the pursuers in any neighborhood of the terminal set. We obtain sufficient conditions for the avoidance of one evader from a group of pursuers in a second-order differential games.
Keywords: differential games, global evasion problem, local evasion problem, positional strategy, phase restrictions. 
@article{IIMI_2013_41_1_a0,
     author = {A. S. Bannikov},
     title = {Some non-stationary problems of group pursuit},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {3--46},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2013_41_1_a0/}
}
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A. S. Bannikov. Some non-stationary problems of group pursuit. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 41 (2013) no. 1, pp. 3-46. http://geodesic.mathdoc.fr/item/IIMI_2013_41_1_a0/