On some properties of the control problem under a program interference in a formalization based on the minimax risk (regret) criterion

An optimal control problem under uncertainty for a system described by an ordinary differential equation with a terminal quality criterion is considered. The control and interference are subject to geometric constraints. The problem is formalized in classes of nonanticipating control strategies and program interferences with the use of constructive ideal motions and the Savage minimax risk (regret) criterion. The properties of the used motion bundles are described and a number of relations characterizing the optimal risk function, which is an element of the formalization, are presented.