Existence of a Value and a Saddle Point in Positional Differential Games for Neutral-Type Systems

Abstract

For a conflict-controlled dynamical system described by functional differential equations of neutral type in Hale’s form, we consider a differential game with a performance index that estimates the motion history realized up to the terminal time and includes an integral estimation of realizations of the players’ controls. The game is formalized in the class of pure positional strategies. The main result is the proof of the existence of a value and a saddle point in this game.