Differential game (DG) of guidance-evasion for a finite time interval is considered;as parameters, the target set (TS) and the set defining phase constraints (PC) are used.Player I interested in realization of guidance with TS under validity PC uses set-valuedquasistrategies (nonanticipating strategies) and Player II having opposite target uses strategieswith nonanticipating choice of correction instants and finite numbers of such instants.On informative level, the setting corresponds to alternative theorem of N. N. Krasovskii andA. I. Subbotin. For position not belonging to solvability set of Player I, determination ofthe least size of neighborhoods for set-parameters under that Player I guarantees guidance(under weakened conditions) is interested. In article, this scheme is supplemented by priorityelements in questions of TS attainment and PC validity; this is realized by special parameterdefining relation for sizes of corresponding neighborhoods. Under these conditions, a functionof the least size of TS neighborhood is defined by procedure used program iteration methodfor two variants. The above-mentioned function is fixed point for one of two used “program”operators. Special type of the quality functional for which values of the above-mentionedfunction coincide with values of the minimax-maximin games is established.
On properties of one functional used in software constructions for solving differential games
