Kapustyan O. A.
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. - 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. - 2002. - 54, № 12. - pp. 1704-1709
We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. In view of this fact, we justify the convergence of approximate controls, switching points, and values of the quality criterion to the exact values of the corresponding variables.