Control packages: an approach to solution of positional control problems with incomplete information

An approach is proposed for solving problems of positional control of a dynamical system under conditions of incomplete information about its current phase states. The basis of this approach is a new notion of control packages, namely, procedures for constructing control programs which are non-anticipatory with respect to the dynamics of observations. For definiteness, the approach is realised for a concrete control problem of guaranteed guidance of a controlled system to a given target set at a fixed moment of time. The main result of the paper states that the indicated problem is soluble in the class of positional strategies if and only if it is soluble in the class of control packages. This result shows a way to reduce control problems in the positional (closed-loop) formulation to control problems in the program (open-loop) formulation. In this sense a methodology for program constructions is developed that is well known in the theory of positional differential games.