Differential Games with Simple Motions on the Manifolds

Abstract

In this chapter differential games are considered, in which players are velocity-controlled points of a Riemannian manifold. The game of pursuit is formulated for the case when pursuer has advantage in speed. Otherwise the game of approach is considered, i.e. the cost function is the minimal distance between the players during infinite time-interval of motion. Despite qualitatively different formulations of the problems their solutions appear to have certain similarities which allow to carry on their considerations in parallel. The essential part of the solution of these games is a singular surface consisting of singular paths (characteristics) and which is the envelope of the regular ones.