Geodesic
Minimax differential game with a fixed end moment
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 3, pp. 77-112

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The minimax game problem of the convergence of a conflict controlled system in a finite-dimensional Euclidean space at a fixed time moment is studied. The issues related to the construction of solutions to the problem are discussed – calculation and approximate calculation of resolvability sets and resolving positional strategies of the first player. The paper develops the method of unification by N.N. Krasovsky. The positional strategy of the first player is studied. This strategy is based on the extreme aiming of the trajectory of a conflict-controlled system at the finite systems of sets in phase space approximating the set of solvability of the convergence problem. The main result of the work is justification of the effectiveness of the extreme aiming strategy for an approximate solution of the problem. Unification constructions were used to substantiate the effectiveness of the strategy complementing the method of unification by N.N. Krasovsky.
Keywords: control, conflict control system, differenital inclusion, game problem of approaching, target set, resolving set, minimax u-stable bridge, minimax u-stable trajectory. 
@article{MGTA_2024_16_3_a4,
     author = {Vladimir N. Ushakov and Alexandr M. Tarasyev and Andrey V. Ushakov},
     title = {Minimax differential game with a fixed end moment},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {77--112},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2024_16_3_a4/}
}
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Vladimir N. Ushakov; Alexandr M. Tarasyev; Andrey V. Ushakov. Minimax differential game with a fixed end moment. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 3, pp. 77-112. http://geodesic.mathdoc.fr/item/MGTA_2024_16_3_a4/