An averaging in linear by control optimal control problem on discret time with variable delay

Abstract

For discrete equations of controlled motion with a varying delay in the state of the system and with a linearly input control parameter, the possibility of applying the averaging method has been proved. For the optimal control problem on the trajectories of such a system with a terminal criterion, the theorem on the proximity of the values of the criterion of the non-averaged optimal control problem on the optimal control of the averaged problem with the optimal value of the criterion of the non-averaged (initial) problem has been proved. That is, the optimal control of the averaged problem is asymptotically optimal control for the original problem. A numerically asymptotic method for solving the optimal control problem of a system in discrete time, which contains a varying delay in the state and linearly depends on the control parameter, has been developed.