ДОСТАТНІ УМОВИ ЗБЛИЖЕННЯ КЕРОВАНИХ ОБ’ЄКТІВ З РІЗНОЮ ІНЕРЦІЙНІСТЮ В ІГРОВИХ ЗАДАЧАХ ДИНАМІКИ

The paper considers the problem of convergence of controlled objects with different inertia in game dynamics problems based on the modern version of the method of resolving functions. For controlled objects with different inertia it is characteristic that on a certain time interval the condition of...

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Bibliographic Details
Date:2020
Main Author: Rappoport, I.S.
Format: Article
Language:English
Published: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
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Online Access:https://jais.net.ua/index.php/files/article/view/505
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Journal Title:Problems of Control and Informatics

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Problems of Control and Informatics
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Summary:The paper considers the problem of convergence of controlled objects with different inertia in game dynamics problems based on the modern version of the method of resolving functions. For controlled objects with different inertia it is characteristic that on a certain time interval the condition of L.S. Pontryagin is not satisfied, which significantly complicates the application of the method of resolving functions to this class of game dynamics problems. We consider the case when the general scheme of the method of resolving functions is based on an analogue of the modified L.S. Pontryagin condition taking into account the terminal set. A method for solving such problems is proposed, associated with the construction of some scalar functions that qualitatively characterize the course of convergence of controlled objects and the efficiency of the decisions made. Such functions are called permissive functions. The attractiveness of the method of resolving functions lies in the fact that it makes it possible to use effectively the modern technique of multivalued mappings in substantiating game constructions and obtaining meaningful results on their basis. In any form of the method of resolving functions, the main principle is the accumulative principle, which is used in the current summation of the resolving function to assess the quality of the game of the first player until a certain threshold is reached. A comparison is made of the guaranteed end times of the game for the considered schemes of approaching controlled objects with different inertia. An example is given.