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JOURNALS // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta // Archive

Izv. IMI UdGU, 2024 Volume 64, Pages 70–96 (Mi iimi471)

MATHEMATICS

Convergence of conflict-controlled systems over a finite period of time

V. N. Ushakova, A. V. Ushakovab, O. A. Kuvshinova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: A nonlinear conflict-controlled system is considered over a finite period of time and in a finite-dimensional Euclidean space. The problem of convergence with a compact target set at a fixed point in time is studied. Within the framework of the convergence problem, one of the key issues is investigated — the approximate construction of sets of solvability of the problem. An approach to approximate construction is discussed, the basis of which is a model that complements N.N. Krasovsky's unification method in the theory of differential games.

Keywords: control, conflict-controlled system, target set, differential inclusion, saddle point in a small game, convergence problem, solvability set of the convergence problem, maximum minimax $u$-stable bridge, maximum minimax $u$-stable path

UDC: 517.957

MSC: 93C15, 49N30

Received: 30.07.2024
Accepted: 27.10.2024

DOI: 10.35634/2226-3594-2024-64-06



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© Steklov Math. Inst. of RAS, 2025