Том 71
№ 1

All Issues

Zheltikov V. P.

Articles: 2
Brief Communications (Russian)

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

Efendiev V. V., Zheltikov V. P.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

Boundary-layer averaging for standard systems with lag

Efendiev V. V., Zheltikov V. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1362–1368

Thekth-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 ? ? 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 ?. We suggest another approach in which the step method is used onlyk times fort? [0,k] and justify the asymptotic method.