КОНФЛІКТНІ СИТУАЦІЇ ЗА УЧАСТЮ ГРУП КЕРОВАНИХ ОБ’ЄКТІВ. Частина 2. ПЕРЕХОПЛЕННЯ ЦІЛЕЙ

• Date: 2020
• Main Author: Chikrii, A.A.
• Format: Article
• Language: English
• Published: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Subjects: Конфліктно-керований процес; умова Понтрягіна; теорема Пшеничного; аполлонієве коло; метод розв’язуючих функцій; правило екстремального прицілювання Красовського; многозначне відображення; стробоскопічна стратегія Хайека; групове та почергове переслідування; ситуація оточення; принцип найкоротшої ламаної
• Online Access: https://jais.net.ua/index.php/files/article/view/493
• Journal Title: Problems of Control and Informatics

An overview of research methods of conflict situations involving groups of controlled objects on each of the counteracting sides is presented. The announced principle of interval decomposition includes solving typical problems of target distribution, group and successive pursuit. To solve them, the method of resolving functions and the extremal aiming rule of N.N. Krasovskii are used. The method of resolving functions, in particular, made it possible to describe the environment situation in the presence of a group of pursuers, as well as in the problems with phase constraints. This made it possible to solve a number of classical problems from the book of R. Isaacs. In the problem of traveling salesman type, namely, in the successive approach, using the law of parallel pursuit and the properties of the Apollonius circle, an algorithm is given for reducing to the finite-dimensional conditional optimization problem. In the positional group pursuit, the ideas of the L.S. Pontryagin maximum principle as well as the B.N. Pshenichnyi scheme associated with the first absorption time are used. The results are illustrated on model examples of game situations. The pursuit processes are implemented in the class of stroboscopic strategies of O. Hajek as well as with the help of quasi-strategies and positional strategies of N.N. Krasovskii.