Krasovskii’s Unification Method and the Stability Defect of Sets in a Game Problem of Approach on a Finite Time Interval

Abstract

A nonlinear conflict-controlled system in a finite-dimensional Euclidean space on a finite time interval is considered, in which the controls of the players are constrained by geometric restrictions. We study a game problem of the approach of the system to a compact target set in the phase space of the system at a fixed instant of time. The problem is investigated in the frame of the positional formalization proposed by N.N. Krasovskii. We study the central property of stability in the theory of positional differential games and, in particular, the generalization of this property such as the stability defect of sets in the space of game positions.