Geodesic
On a~pursuit-evasion problem under a~linear change of the pursuer resource
Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 159-171

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We study a pursuit-evasion problem in the case when an integral constraint is imposed on the pursuer control class which is a generalization of integral as well as geometric constraints and only a geometric constraint is imposed on the evader control class. We prove the theorem of alternative. The optimal pursuit problem is solved by a generalized parallel pursuit strategy, and lower bounds for the distance between the pursuer and the evader are established in the pursuit problem. 
@article{MT_2012_15_2_a9,
     author = {B. T. Samatov},
     title = {On a~pursuit-evasion problem under a~linear change of the pursuer resource},
     journal = {Matemati\v{c}eskie trudy},
     pages = {159--171},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2012_15_2_a9/}
}
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B. T. Samatov. On a~pursuit-evasion problem under a~linear change of the pursuer resource. Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 159-171. http://geodesic.mathdoc.fr/item/MT_2012_15_2_a9/