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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., UDC 517.9 Introduction In some applications, as a result of modeling of controlled processes, the researchers get functional differential equations with small parameters. Moreover, if the corresponding system is nonlinear, [...]

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]

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.