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Abstract: Two differential games of the simple pursuit of a group of evaders by a group of pursuers are considered. The first problem is devoted to the pursuit of a group of rigidly co-ordinated evaders by a group of pursuers with equal possibilities for all participants. It is supposed that the evaders remain in the bounds of the convex polyhedral set, terminal sets are convex compacts and the aim of the group of pursuers is to capture at least one evader. The solvability conditions of the problem of pursuit and the problem of evasion are obtained in the terms of initial positions and parameters of the game.
The second problem is devoted to the pursuit of a group of evaders by a group of pursuers under condition that the evaders use program strategies and one pursuer can catch only one evader. The aim of a group of pursuers is to capture a specified number of evaders. Terminal sets are convex compacts, the set of possible controls is an arbitrary convex compact. Necessary and sufficient solvability conditions of the problem of pursuit are obtained.

Keywords: differential game, simple motion, group pursuit, rigidly co-ordinated evaders.

Received: 19.10.2011

Citation: D. V. Sakharov, “On two differential games of simple group pursuit”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 1, 50–59

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This publication is cited in the following articles:

1. D. V. Sakharov, “Dve zadachi prostogo gruppovogo presledovaniya”, Izv. IMI UdGU, 2012, no. 1(39), 121–122  
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7. N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache prostogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 193–198      
8. A. I. Machtakova, “Presledovanie zhestko skoordinirovannykh ubegayuschikh v lineinoi zadache s drobnymi proizvodnymi i prostoi matritsei”, Izv. IMI UdGU, 54 (2019), 45–54      
9. N. N. Petrov, A. Ya. Narmanov, “Multiple Capture of a Given Number of Evaders in a Problem with Fractional Derivatives and a Simple Matrix”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S105–S115          
10. Petrov N.N., Solov'eva N.A., “Multiple Capture of Given Number of Evaders in Linear Recurrent Differential Games”, J. Optim. Theory Appl., 182:1, SI (2019), 417–429          
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