On a Problem of Guarantee Optimization in Time-Delay Systems*

A control problem under conditions of disturbances is considered for a linear time-delay dynamical system. The goal of the control is to minimize a non-terminal quality index that evaluates a motion history and realizations of control and disturbance actions. The control problem is posed within the game-theoretical approach. For calculating the optimal guaranteed result of the control and constructing a control scheme that ensures this result, two methods are proposed. The first one is based on an appropriate approximation of the quality index. The second one is based on a finite-dimensional approximation of the dynamical system. Both methods allow us to reduce the control problem to high-dimensional auxiliary differential games without delays and with terminal quality indices. An illustrative example is considered, simulations results are given.