On Basic Equation of Differential Games for Neutral-Type Systems

Abstract

For a conflict-controlled dynamical system described by neutral-type functional differential equations in Hale’s form, a differential game is considered in the classes of control strategies with a guide for a minimax-maximin of the quality index, which evaluates the system’s motion history implemented by the terminal time moment. The differential game is associated with the Cauchy problem for a functional Hamilton-Jacobi type equation in coinvariant derivatives. It has been proven that the game value functional coincides with the minimax solution of this problem. A method of constructing the optimal strategies of players is given. The approximation by ordinary Hamilton-Jacobi equations in partial derivatives is proposed for this functional Hamilton-Jacobi equation in coinvariant derivatives.