Conflict Situations Involving Controlled Object Groups. Part 1. Collision Avoidance

The article provides an overview of the game problems of pursuitevasion with the participation of groups of controlled objects. In the first part of the review, the current state of the problem is examined. The main results concerning the methods of maneuvering around, deviation in direction, as well as the method of invariant subspaces, are presented. Rough and subtle cases of the problem of collision avoidance, conditions of higher order are explored. The problem of evasion from a group of pursuers and during interaction of the groups is considered. Several general results for nonlinear systems are formulated, problem statements are given for many specific linear problems, given the complexity of the general problem. Most of the results relate to the global Pontryagina-Mishchenko problem and several others relate to the local evasion problem, being a development of the Pshenicnyi theorem. Collision avoidance processes are carried out in the classes of ϵ-strategies, ϵ-counter-strategies, and under positional information. The main apparatus for substantiating mathematical constructions are the methods of nonlinear and convex analysis, the theory of set-valued mappings. © 2020 Begell House Inc.. All rights reserved.