Open AccessOn properties of one functional used in software constructions for solving differential games
Author(s) -
А. Г. Ченцов
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210410
Subject(s) - minimax , realization (probability) , limit (mathematics) , position (finance) , differential game , function (biology) , mathematics , differential (mechanical device) , trajectory , nonlinear system , space (punctuation) , set (abstract data type) , function space , mathematical optimization , computer science , mathematical analysis , physics , statistics , finance , quantum mechanics , astronomy , evolutionary biology , programming language , economics , biology , operating system , thermodynamics
Nonlinear differential game (DG) is investigated; relaxations of the game problem of guidance are investigated also. The variant of the program iterations method realized in the space of position functions and delivering in limit the value function of the minimax-maximin DG for special functionals of a trajectory is considered. For every game position, this limit function realizes the least size of the target set neighborhood for which, under proportional weakening of phase constraints, the player interested in a guidance yet guarantees its realization. Properties of above-mentioned functionals and limit function are investigated. In particular, sufficient conditions for realization of values of given function under fulfilment of finite iteration number are obtained.