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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2021 Volume 212, Number 9, Pages 40–74 (Mi sm9496)

This article is cited in 6 papers

Two game-theoretic problems of approach

A. A. Ershov, A. V. Ushakov, V. N. Ushakov

N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: A nonlinear conflict control system in a finite-dimensional Euclidean space on a finite time interval is considered. Two interrelated game-theoretic problems of making a system approach a compact set at a fixed moment of time are studied. A method for constructing approximate solutions to game problems of approach is presented. Most attention is paid to problems related to constructing approximations of the solvability sets of game problems in the phase space.
Bibliography: 35 titles.

Keywords: control system, target set, game-theoretic problem of approach, differential inclusion, solvability set.

UDC: 517.978.2+517.977.58

MSC: Primary 49N70, 91A23; Secondary 93C10

Received: 25.08.2020 and 30.11.2020

DOI: 10.4213/sm9496


 English version:
Sbornik: Mathematics, 2021, 212:9, 1228–1260

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© Steklov Math. Inst. of RAS, 2025