Sukretna A. Approximate averaged bounded synthesis for distributive systems

The thesis is devoted to construction of approximate averaged synthesized controls for some optimal control problems for distributed systems with rapidly oscillating coefficients. Three problems are considered: the optimal control problem for parabolic boundary-value problem on finite time interval, the problem of optimal stabilization for parabolic process and the problem of optimal control for the wave equation. For each of the considered problems in the case where the control reaches a restriction and there is an unique switching point the optimal control in the form of feed-back is constructed. This control takes the form of series by the eigenfunctions of the operator corresponding to boundary-value problem and irregularly depends on small parameter and is not suitable for practical applications. Therefore by application of the conception of G - convergence and averaged matrix some algorithms of averaged approximate synthesis are proposed. For these objects are proved that optimal and approximate controls, corresponding to state of controlled system and value of quality criteria on these controls are close, so correctness of constructed controls is proved. For the optimal control problem for the wave equation similar results are obtained in the case of failing restrictions on the control.