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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2009 Volume 15, Number 4, Pages 146–166 (Mi timm433)

This article is cited in 8 papers

An approach-evasion differential game: Stochastic guide

N. N. Krasovskii, A. N. Kotel'nikova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A positional differential game of the approach-evasion of a conflict-controlled motion and a goal set within a given set is considered. Use is made of a solution of the associated boundary-value problem for a parabolic equation degenerating as the diffusion term vanishes to a Hamilton–Jacobi type equation, which is typical for techniques in the theory of differential games. Based on this, a control scheme with a stochastic guide is developed.

Keywords: approach-evasion alternative, strategy, probabilistic process, Ito equation, Lyapunov function.

UDC: 517.977

Received: 15.05.2009


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2010, 269, suppl. 1, S191–S213

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