Guarantee optimization in functional-differential systems with a control aftereffect

The problem of calculating the optimal guaranteed result and constructing a control strategy that ensures this result is considered in the case of a dynamical system that is controlled under conditions where there is interference and which contains an aftereffect with respect to the state and the control. The optimizing factor consists of two terms. The first term estimates the deviations of the trajectory of motion of the system at specified times from the specified targets and the second term is an integral estimate of the forms of the control and the interference. By a functional treatment of the control process based on an original prediction of the motions, the problem is reduced to finding the value and the saddle point in a differential game without an aftereffect and with a terminal estimate of the motion. The value is calculated by the method of downwards convex hulls of auxiliary functions from stochastic program synthesis. The optimal strategies forming the saddle point are constructed by the extremum shift method. The results of numerical experiments are presented.