The Partial Averaging of Fuzzy Differential Inclusions on Finite Interval

The substantiation of a possibility of application of partial averaging method on finite interval for differential inclusions with the fuzzy right-hand side with a small parameter is considered

AN EXISTENCE AND UNIQUENESS THEOREM TO THE CAUCHY PROBLEM FOR GENERALISED SET DIFFERENTIAL EQUATIONS

Abstract. In this paper the concept of generalized differentiability for set-valued mappings proposed by A.V. Plotnikov, N.V. Skripnik is used. The generalized set-valued differential equations with generalized derivative are considered, the existence and uniqueness theorem is proved

Piecewise Constant Control Set Systems

Abstract In this article we prove that for any measurable admissible control ( ) w ⋅ and for any 0 ε > there exists piecewise constant admissible control ( ) w ⋅ such that for set solutions of control set system are ε -neighbouring

Averaging of the Fuzzy Differential Equations

Abstract In this article we prove the substantiation of the method of full averaging for the fuzzy differential equations with small parameter on the metric space (E n ; D). Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging. c 2012 World Academic Press, UK. All rights reserved. Keywords: fuzzy differential equation, differential equations with small parameter, averaging scheme Instroduction The absence of exact universal research methods for nonlinear systems has caused the development of numerous approximate analytic and numerically-analytic methods that can be realized in effective computer algorithms. Many important problems of analytical dynamics are described by the nonlinear mathematical models that as a rule are presented by the nonlinear differential or the integro -differential equations. The absence of exact universal research methods for nonlinear systems has caused the development of numerous approximate analytic and numerically-analytic methods that can be realized in effective computer algorithms. The averaging methods combined with the asymptotic representations (in Poincare sense) began to be applied as the basic constructive tool for solving the complicated problems of analytical dynamics described by the differential equations. Plotnikov, A.N. Filatov, etc. (see [2, In recent years, the fuzzy set theory introduced by Zadeh [36] has emerged as an interesting and fascinating branch of pure and applied sciences. The applications of fuzzy set theory can be found in many branches of science as physical, mathematical, differential equations and engineering sciences. Recently there have been new advances in the theory of fuzzy differential equations. The theory of fuzzy differential equations has been studied by many authors Preliminaries Let (conv(R n ), h) denote the family of all nonempty compact convex subsets of R n . Let A and B be two nonempty bounded subsets of R n . The distance between A and B is defined by the Hausdorff metri