Abstract
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 second 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 case, 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 maximun control strategies, which is convenient for numerical implementation, is obtained from this treatment and from the construction of hulls, convex upwards, of auxiliary functions from the method of stochastic program synthesis. The results of a numerical experiment are presented.
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