A Hamilton-Jacobi type equation in control problems with hereditary information

In the problem of conflict control with a each of information, formalized as a differential game [1-11] in a system with delays, a Hamilton-Jacobi type equation is written for the value functional using the concept of co-invariant derivatives [12]. Like that set out earlier [10], the corresponding generalized minimax solution of this equation is considered. Control strategies extremal to the given solution are constructed. It is proved that these strategies form a saddle point bf the game, while the value functional is identical with the minimax solution of the equation. (C) 2000 Elsevier Science Ltd. All rights reserved.