A minimax control problem with a performance index which is the sum of two
terms is considered for a system with a delay. The first of these two terms
in the Euclidean norm of the set of deviations of the motion of the system
at specified instants of time from the stipulated objectives, while the se
cond term is an integral-quadratic penalty which is imposed on the form of
the control actions. The problem arises in a differential game. In this cas
e, the history of the motion serves as the information for the strategies.
A functional treatment of the control process in question is given which is
based on an original prediction of the motion. A procedure for calculating
the value of the game and for constructing minimax and maximin control str
ategies, which is convenient for numerical implementation, is obtained from
this treatment and from the construction of hulls, convex upwards, of auxi
liary functions from the method of stochastic program synthesis. The result
s of a numerical experiment are presented. (C) 1998 Elsevier Science Ltd. A
ll rights reserved.