
Minimax Theory and its Applications 05 (2020), No. 2, 275304 Copyright Heldermann Verlag 2020 Relaxation of a Dynamic Game of Guidance and Program Constructions of Control Alexander G. Chentsov Krasovskii Inst. of Mathematics and Mechanics, UB RAS, Ekaterinburg 620108, Russia chentsov@imm.uran.ru Daniel M. Khachay Krasovskii Inst. of Mathematics and Mechanics, UB RAS, Ekaterinburg 620108, Russia daniil.khachay@gmail.com The natural relaxation of guidance problem is considered. Namely, for fixed closed sets considered as parameters (target set and the set defining state constraints), we consider the similar guidance problem for εneighborhoods of these sets. We are interested to find the smallest size ε of these neighborhoods for which the player I can solve his guidance problem in class of generalized setvalued nonanticipating strategies. For the construction of solution, the Program Iterations Method is used. We obtain the abovementioned smallest size as a position function. For determination of this function, iterative procedure operating in the function space is used. Also, it is shown that desired function is the fixed point of operator defining the iterative procedure. Keywords: Pursuitevasion differential game, program iteration method, guaranteed result. MSC: 49J15, 49K15, 93C15, 49N70. [ Fulltextpdf (198 KB)] for subscribers only. 