ПРО ГАРАНТОВАНИЙ РЕЗУЛЬТАТ В ІГРОВИХ ЗАДАЧАХ ЗБЛИЖЕННЯ КЕРОВАНИХ ОБ’ЄКТІВ

• Datum: 2025
• 1. Verfasser: Rappoport, I.S.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Schlagworte: квазілінійна диференціальна гра; багатозначне відображення; вимірний селектор; стробоскопічна стратегія; розв’язувальна функція
• Online Zugang: https://jais.net.ua/index.php/files/article/view/462
• Назва журналу: Problems of Control and Informatics

The problem of a guaranteed result in game problems of approach of controlled objects is considered. A method is proposed for solving such problems associated with the construction of some scalar functions that qualitatively characterize the course of approach of controlled objects and the effectiveness of decisions made. Such functions are called resolving functions. 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 selectors in the justification of game constructions and obtaining meaningful results on their basis. In all forms 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 up to a certain threshold value. In contrast to the main scheme of the mentioned method, the case is considered 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 approach of controlled objects is given. An illustrative example of the approach of controlled objects approach with simple movement is given in order to obtain explicitly the upper and lower resolving functions, which make it possible to conclude that the game can be terminated in a case when the Pontryagin condition does not hold.