THE PROBLEM OF COMPUTING THE VALUE OF A DIFFERENTIAL GAME FOR A POSITIONAL FUNCTIONAL

A dynamical system driven by controls and uncontrollable noise is cons idered in a game-theoretic setting [1-8]. The problem of feedback cont rol in which the performance index is a positional functional of the m otion 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 d ifferential game. Irrespective of the number of dimensions in the init ial problem, as dictated by the structure of the performance index, th e proposed procedure reduces to the problem of the successive construc tion of the upper convex hulls of certain auxiliary functions in domai ns whose dimension does not exceed that of the phase vector of the sys tem. (C) 1998 Elsevier Science Ltd. All rights reserved.