Control of a delayed standard system (Q1364125)

The article considers optimal control of a standard system with delay on an asymptotically long time interval (with time the independent variable). If control is an admissible function of time, then under sufficiently general conditions the delay is essential only near the initial point. Similarly in the corresponding boundary-value problem of the maximum principle, where both delay and anticipation are observed, these facts essentially affect the solution only in the neighborhood of boundary points. The original problem thus can be simplified by the averaging method, and under certain conditions on the properties of the original problem we prove closeness of the functionals on the original optimal path and the averaged path.