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自动化与信息科学期刊

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ISSN 打印: 1064-2315

ISSN 在线: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

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Sufficient Conditions for the Approach of Controlled Objects with Various Inertia in Game Dynamics Problems

卷 52, 册 11, 2020, pp. 28-47
DOI: 10.1615/JAutomatInfScien.v52.i11.30
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摘要

The paper considers the approach problem of controlled objects with different inertia in game dynamics problems based on modern version of the resolving functions method. For controlled objects with different inertia it is characteristic that on a certain time interval the Pontrygin condition is not fulfilled that significantly complicates the application of the resolving functions method to this class of game dynamics problems. Consideration is given to the case when the general scheme of the resolving functions method is based on the analog of the modified Pontryagin condition taking into account the terminal set. For solving such problems the paper proposes the method associated with constructing some scalar functions which qualitatively characterize the course of controlled objects approach and the efficiency of the decisions made. Such functions are called resolving. The attractiveness of the resolving functions method lies in the fact that it enables one to use effectively the modern technique of multivalued mappings to substantiate game construction and to obtain meaningful results on their basis. In any forms of the resolving functions method the main principle is the accumulative one used in the current summation of the resolving function to estimate the quality of the first player game until a certain threshold is reached. The guaranteed game termination times for the considered schemes of controlled objects approach with different inertia are compared. The example is given.

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