2019
Том 71
№ 11

# Zheltikov V. P.

Articles: 2
Brief Communications (Russian)

### Averaging of boundary-value problems of control over a standard system with delay

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.

Article (Russian)

### Boundary-layer averaging for standard systems with lag

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.