Geodesic
The method of resolving functions for solving a pursuit problem with integral constraints on player controls
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 103-118

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In this paper, we study pursuit game problems described by a system of equations with a retarded argument under integral constraints on the players' controls. The proposed scheme uses the ideas of the method of resolving functions. Modifications of methods (i.e., the first and so-called third methods) [1,3,12] of pursuit are proposed in the case when integral constraints are imposed on the players' controls. Sufficient conditions are obtained for the possibility of completing the pursuit in a finite time.
Keywords: differential game, pursuit game, integral constraint, resolving function, conflict-controlled process, multivalued mapping, control, pursuer, evader. 
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     title = {The method of resolving functions for solving a pursuit problem with integral constraints on player controls},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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N. A. Mamadaliev; Kh. Ya. Mustapokulov; G. M. Abdualimova. The method of resolving functions for solving a pursuit problem with integral constraints on player controls. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 103-118. http://geodesic.mathdoc.fr/item/VUU_2023_33_1_a6/