Minimax Differential Game with a Fixed End Moment

Abstract

The minimax game problem of approach of a conflict-controlled system in a finite-dimensional Euclidean space at a fixed time moment is studied. Issues related to the construction of solutions to the problem are discussed, namely, the calculation and approximate calculation of solvability sets and the first player’s solving feedback strategies. N.N. Krasovskii’s method of unification is further developed. A feedback strategy of the first player based on the extreme aiming of the system’s trajectory at finite systems of sets in the phase space that approximate the solvability set of the approach problem is studied. As the main result, we justify the effectiveness of the extreme aiming strategy for an approximate solution of the problem. The effectiveness of the strategy is justified using unification constructions supplementing Krasovskii’s unification method.