Guarantee Optimization in Functional Differential Systems with Control Delays*

For a control dynamical system with disturbances, and with delays in state and control variables, the problem of calculating the optimal guaranteed result and a control strategy that provides this result is considered. The quality of the control process is evaluated by the sum of two terms. The first term is the Euclidian norm of the set of deviations of the system motion at the given instants of time from the given targets. The second term is an integral-quadratic estimation of the control and disturbance realizations. On the basis of an appropriate motion prediction the problem is reduced to calculating the value and the minimax strategy in the auxiliary differential game without delays and with the terminal payoff. The corresponding computational procedure is elaborated. The results of numerical experiments are given.