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We study the problem of optimal control for a class of evolutionary parabolic functional-differential equations in Banach spaces. Sufficient conditions for the existence of an optimal pair are established. Note that the main problem of optimal control is considered up to the time of exit of the solution from the domain, which distinguishes the analyzed problem from the other investigations. [ABSTRACT FROM AUTHOR]

We consider the optimal control problem for systems with infinite memory whose models are described by functional-differential equations. We prove the theorem on existence, uniqueness, and continuity of solutions for a system of functional-differential equations in which the delay interval is infinitely large. Sufficient conditions for the existence of optimal controls in the optimal control problems for systems with infinite memory are obtained in terms of the right-hand sides of the equations of motion and the function of performance criterion. [ABSTRACT FROM AUTHOR]

We study the optimal control problem for a system of differential inclusions with rapidly oscillating coefficients on the semiaxis. For this purpose, we use the averaging method. The solvability of the original exact problem and the corresponding averaged problem is substantiated. It is proved that the optimal controls and optimal trajectories of solutions of the exact problem converge to the optimal control and optimal trajectory of solutions of the averaged problem. It is also shown that the optimal control of the averaged problem is "almost" optimal for the original exact problem. [ABSTRACT FROM AUTHOR]

For nonlinear controlled functional-differential systems, the possibility of applying of the method of averaging on a finite interval without the condition of constancy of the asymptotic control is proved and an algorithm for the construction of the corresponding controls over the original and averaged systems is proposed. [ABSTRACT FROM AUTHOR]

We consider optimal control problems for nonlinear systems whose dynamics depends on the maximum of the control function and the maximum of the state over a certain time interval of prehistory. We are interested in the approximation of solutions for this kind of problems. An averaging method is developed for this purpose. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Averaging method is applied to the nonlinear and linear (with respect to control) problems of optimal control on the semiaxis with small parameter and rapidly oscillating coefficients. It is shown that the solutions of the exact problem converge to the solutions of the averaged problem. [ABSTRACT FROM AUTHOR]

We consider a system of discrete equations containing variable delays and apply the averaging method to find the solution of this system. We propose new procedures for taking into account a given variable delay in the solution of the averaged system. It is shown that the solutions of the averaged and original systems are close. [ABSTRACT FROM AUTHOR]

The article focuses on the schemes of complete and partial averaging on a finite interval for fuzzy differential equations with delay. It states that Zadeh's work in 1965 laid the foundation for the development of the theory of fuzzy sets. The notion of derivative and integral for fuzzy mappings as well as fuzzy differential equations are examined.