Efendiev V. V.
Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1265-1275
We justify the averaging method for systems with delay described by both “slow” and “fast” variables. The results obtained are applied to the analysis of one problem in control theory.
Ukr. Mat. Zh. - 1996. - 48, № 4. - pp. 548-553
For the terminal problem of optimal control over systems of standard form with constant delay, according to the Pontryagin maximum principle, we study a boundary-value problem with deviating arguments with delay and anticipation. We justify an averaging method for an asymptotic solution of the boundary-value problem obtained.
Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1362–1368
The $k$-th-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter $ε ≪ 1$, then the use of the step method for finding the solution is connected with cumbersome calculations because the number of required steps is inversely proportional to $ε$. We suggest another approach in which the step method is used only $k$ times for $t \in [0,k]$ and justify the asymptotic method.