Geodesic
Stochastic guide for a~time-delay object in a~positional differential game
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 97-104

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A positional differential time-optimal game is considered for a conflict-controlled time-delay object. Minimax and maximin feedback controls are constructed within a scheme that includes an intermediate model object described by an ordinary differential equation and a stochastic guide described by the Ito differential equation. The motion of the guide is based on the real-time solution of a sequence of auxiliary boundary value problems for a parabolic equation with degenerate diffusion term.
Keywords: time-delay object, minimax-maximin time of rendezvous, stochastic guide. 
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     title = {Stochastic guide for a~time-delay object in a~positional differential game},
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N. N. Krasovskii; A. N. Kotel'nikova. Stochastic guide for a~time-delay object in a~positional differential game. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 97-104. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a9/