In this paper, we study optimal control problems for stochastic semilinear partial differential equations, which lack the maximum principle, and whose coefficients do not have bounded Frechet derivatives. We propose an approximation scheme for the corresponding optimization problem, and prove convergence of the approximating solutions on both finite and infinite time intervals.

For the optimal control problem of an integro-differential system with rapidly oscillating coefficients on the infinite interval, the convergence of optimal controls, trajectories, and quality criterion from the original problem to the corresponding triple of solutions of the averaged problem is established.

We study global resolvability for parabolic inclusions with an upper semicontinuous multi-valued right-hand part of more than linear growth. Theorems about the existence of global mild solutions in different phase spaces are proved. Limit sets for the obtained global solutions in the corresponding phase spaces are investigated.

In the given paper we are dealing with an optimal control problem on the semi-axis. We have stated the connection between solutions to optimal control problems on time scales and to the corresponding problem on real semi-axis. A new method is proposed for constructing a minimizing sequence for a problem on the semi-axis.

In this paper we study functional-differential equations on the semi-axis, which are non-linear with respect to the phase variables and linear with respect to the control.Sufficient conditions for existence of optimal control in terms of the right-hand side and the quality criterion are obtained.Relation between the solutions of the problems on infinite and finite intervals is studied and results that about these connections are proven.

In this paper we study the connection between the existence of bounded (on real axis) solutions of differential equations and the corresponding difference equations. We obtain the conditions, under which the existence of bounded solutions of differential equations implies the existence of bounded solution of difference equation and vice versa.

We consider linear and nonlinear stochastic optimal control problems with linear quadratic functional. For such problems, by the method of dynamic programming, we prove the existence of optimal control in the form of feedback control.