Open AccessRelaxation of pursuit-evasion differential game and program absorption operator
Author(s) -
А. Г. Ченцов,
Daniel Khachay
Publication year - 2020
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm200106
Subject(s) - corollary , differential game , relaxation (psychology) , operator (biology) , evasion (ethics) , position (finance) , function (biology) , mathematics , pursuit evasion , differential (mechanical device) , computer science , mathematical optimization , discrete mathematics , physics , psychology , social psychology , biochemistry , chemistry , immune system , finance , repressor , evolutionary biology , biology , transcription factor , economics , immunology , gene , thermodynamics
We consider some natural relaxation of pursuit-evasion differential game. For two closed sets, which are parameters, similar guidance problem for $\varepsilon$-neighborhoods is being solved. We are interested in finding a minimal size of such neighborhoods, which allows player I successfully solve his guidance problem in the class of generalized non-anticipating strategies. To resolve above-mentioned differential game, a modification of Program Iterations Method is implemented. Size of the neighborhoods is found as a position function and it's defined by application of special iterative procedure further below. As a corollary, it is shown that desired function is a fixed point of the open-loop operator, which defines the procedure.