Geodesic
Relaxation of pursuit-evasion differential game and program absorption operator
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 1, pp. 64-91

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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.
Keywords: pursuit-evasion differential game, program iterations method, guaranteed result. 
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     title = {Relaxation of pursuit-evasion differential game and program absorption operator},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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A. G. Chentsov; D. M. Khachai. Relaxation of pursuit-evasion differential game and program absorption operator. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 1, pp. 64-91. http://geodesic.mathdoc.fr/item/VUU_2020_30_1_a5/