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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v52.i3.40
pages 48-64

On Guaranteed Result in Game Problems of Controlled Objects Approach

Iosif S. Rappoport
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev


The problem of a guaranteed result in game problems of controlled objects approach is considered. For solving such problems a method is proposed associated with the construction of some scalar functions that qualitatively characterize the course of controlled objects approach and the effectiveness of decisions made. Such functions are called the resolving ones. The attractiveness of the method of resolving functions is that it allows you to use effectively the modern technique of multi-valued mappings and their selector in the justification of the game constructions and obtaining meaningful results on their basis. In all forms of the method of resolving functions the main principle is the accumulative one which is used in the current summation of the resolving function to assess the quality of the game of the first player up to a certain threshold value. In contrast to the main scheme of the mentioned method consideration is given to the case when the classical Pontryagin condition does not hold. In this situation instead of the Pontryagin selector, which does not exist, a certain shift function is considered, and with its help special multi-valued mappings are introduced. They generate upper and lower resolving functions of two types with the help of which the sufficient conditions for completing a game in a certain guaranteed time are formulated. The comparison of guaranteed times for different schemes of controlled objects approach is given. An illustrative example of controlled objects approach with simple movement is given in order to obtain explicitly the upper and lower resolving functions that makes it possible to conclude that the game can be terminated in a case when the Pontryagin condition does not hold.


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