Quasi-Linear Differential-Deference Game of Approach

Abstract

The paper is devoted to the games of approach. We consider a controlled object whose dynamics is described by the linear differential system with pure time delay or the differential-difference system with commutative matrices in Euclidean space. The approaches to the solutions of these problems are proposed which based on the Method of Resolving Functions and the First Direct Method of L.S. Pontryagin. The guaranteed times of the game termination are found, and corresponding control laws are constructed. The results are illustrated by a model example.