МЕТОД РОЗВ’ЯЗУВАЛЬНИХ ФУНКЦІЙ В ЗАДАЧІ ГРУПОВОГО ПЕРЕСЛІДУВАННЯ З ТЕРМІНАЛЬНОЮ ФУНКЦІЄЮ ПЛАТИ ТА ІНТЕГРАЛЬНИМИ ОБМЕЖЕННЯМИ НА КЕРУВАННЯ

• Дата: 2025
• Автор: Rappoport, J.S.
• Формат: Стаття
• Мова: English
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Теми: лінійна диференціальна гра; термінальна функція плати; інтегральні обмеження; багатозначне відображення; вимірний селектор; стробоскопічна стратегія; групове переслідування
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/636
• Назва журналу: Problems of Control and Informatics

A method is proposed for solving game dynamics problems with a terminal pay off function and integral constraints on controls, which consists in systematically using the ideas of Fenhel-Moreau in relation to the general scheme of the method of resolving functions. The essence of the proposed method lies in the fact that the resolving function can be expressed through the function conjugate to the pay off function and, using the involute of the conjugation operator for a convex closed function, to obtain a guaranteed estimate of the terminal value of the pay off function, which is represented through the paying off value at the initial time and the integral of the resolving function. The main feature of the method is the cumulative principle, which is used in the current summation of the resolving function for assessing the quality of the game until a certain threshold value is reached. The paper considers linear differential games of group pursuit with a terminal pay off function and integral constraints on controls. Sufficient conditions for termination of the game for a finite guaranteed time in the class of quasistrategies are formulated. Two schemes of the method of resolving functions are proposed that ensure without additional assumptions the completion of the game for the final guaranteed time in the class of stroboscopic strategies. The guaranteed times for various schemes of the resolving-functions method are compared.