Sukretna A. V.
Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 654-661
For a problem of optimal stabilization of solutions of a nonlinear parabolic boundary-value problem with small parameter of a nonlinear summand, we justify the form of approximate regulator on the basis of the formula of optimal synthesis of the corresponding linear quadratic problem.
Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1094–1104
We consider the problem of optimal control for the wave equation. For the formulated problem, we find the optimal control in the form of a feedback in the case where the control reaches a restriction, construct an approximate control, and substantiate its correctness, i.e., prove that the proposed control realizes the minimum of the quality criterion.
Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1384–1394
For a problem of optimal control for a parabolic equation, in the case of bounded control, we construct and justify an approximate averaged control in the form of feedback.
Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 612-620
For a wave equation, we determine an optimal control in the feedback form and prove the convergence of the constructed approximate control to the exact one.