2019
Том 71
№ 11

# Efendiev V. V.

Articles: 3
Article (Russian)

### Averaging of Systems with Slow Variables

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.

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.