Some questions of differential game theory with phase constraints

Differential game (DG) of guidance-evasion is considered; moreover, its relaxations constructed with due account for priority considerations in the implementation of target set (TS) guidance and phase constraints (PC) validity are considered. We suppose that TS is closed in a natural topology of position space. With respect to the set that defines PC, it is postulated that the sections corresponding to time fixing are closed. For this setting, with the use of program iteration method (PIM), a variant of alternative for some natural (asymmetric) classes of strategies is established. A scheme of relaxation for the game guidance problem with nonclosed (in general case) set defining PC is considered. Under relaxation construction, reasons connected with priority in the implementation of guidance to TS and PC validity are taken into account (the case of asymmetric weakening of conditions of game ending is investigated). A position function is introduced, values of which (with priority correction) play the role of an analogue of least size for neighborhoods of TS and set defining PC under which it is possible to get a guaranteed solution of a relaxed problem of a player interested in approaching with TS while observing PC. It is demonstrated that the value of given function (when fixing the position of the game) is a price of DG for minimax-maximin quality functional which characterizes both the “degree” of approaching with TS and the “degree” of observance of initial PC.

Relaxation of the game problem of guidance connected with alternative in guidance-evasion differential game

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.

Journey Toward Evidence-Based Status: Seeking Admission to Formal Program Registries

In the past two decades, evidence-based status has been a coveted credential for many nonprofit organizations hoping to legitimize their programs or interventions. Several formal registries exist to provide a collection of health and prevention programs evaluated by experts and deemed “evidence-based.” While registries offer positive benefits like allowing for a centralized listing of approved programs, there have been concerns about issues pertaining to the process of obtaining the evidence-based credential. Namely, some of the criticisms include the use of inappropriate study designs, the lack of consistent evaluation of evidence provided in support of programs, as well as program creators being involved in the evaluation that ultimately shows positive program effects. Using focus groups of prevention specialists, this study explores the quest for evidence-based status. The results show themes of vindication, acting as a resource, and perceptions of relevant others informing the deeper meaning of motivation for pursuit of evidence-based status. Additionally, emergent themes of program iteration and evolution inform program preparation. The article shows that while placement on an evidence-based registry is a highly sought-after achievement, many program creators fail to understand the evaluation process for admittance as well as the potential criticisms of the lists.