| Abstract: | A dynamical system driven by controls and uncontrollable noise is considered in a game-theoretic setting [1–8]. The problem of feedback control in which the performance index is a positional functional of the motion of the system [8–11] is investigated. On the assumption that the structure of the functional satisfies reasonably general conditions, a procedure is proposed for computing the value of the corresponding differential game. Irrespective of the number of dimensions in the initial problem, as dictated by the structure of the performance index, the proposed procedure reduces to the problem of the successive construction of the upper convex hulls of certain auxiliary functions in domains whose dimension does not exceed that of the phase vector of the system. |
