Solution methods for two-player differential games

A numerical solution method is proposed for the pursuit-and-evasion game in which the terminal set is the sum of a two-dimensional convex compactum and a linear subspace of codimension 2. The “convexification method” is applied to compute the alternated sums. Simple switching lines are constructed for the case when the set of constraints on pursuer controls is a polyhedron. These simple switching lines essentially simplify the construction of a pursuit strategy in the convex programming problem. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 49–66, 1994.