Dynamical Optimization of Systems with Control Delays*

For a linear dynamical systems with disturbances and control delays, the minimax feedback control problem is considered. The quality index under optimization is the Euclidian norm of the set of motion deviations at the given instants from the given targets. On the basis of a functional interpretation, relying on an appropriate motion prediction, the problem is reduced to an auxiliary differential game without control delays and with the terminal payoff. The value of this game can be calculated by constructing upper convex hulls of some functions from the stochastic programming method. The desirable minimax strategy is formed by the method of extremal shift to accompanying points. An illustrative example is considered. Results of numerical simulations are given.