On basic equation of differential games for neutral-type systems (Q2226141)

The authors consider a differential game in the classes of control strategies with a guide for a minimax-maximin of the quality index, for a conflict-controlled dynamical system described by neutral-type functional differential equations in Hale's form. It 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. A method of constructing the optimal strategies of players is given; and the approximation by ordinary equations is proposed for this functional equation in coinvariant derivatives.