Averaging of fuzzy systems (Q2417292)

The asymptotic methods aimed at the investigation of nonlinear differential equations occupy a central place in the nonlinear mechanics. Krylov and Bogolyubov were the first who developed a general algorithm and proved the theorem on closeness of the solutions of exact and averaged systems. Later these results were generalized by Mitropol'skii, Samoilenko, Akulenko, Volosov, Grebennikov, Krasnosel'kii, Krein, Moiseev, Perestyuk, Plotnikov, Filatov, Chernous'ko, and other researchers to nonlinear equations with slowly varying coefficients, multifrequency systems of partial differential equations, difference equations, equations with discontinuous right-hand sides, impulsive differential equations, equations with delay, stochastic equations, equations in infinite-dimensional spaces, differential inclusions, differential equations and inclusions with Hukuhara derivative, set-valued integral and integro-differential equations, quasidifferential equation, etc. In this survey, the authors present the results on justifying the averaging method for some classes of fuzzy systems: fuzzy differential equations, fuzzy differential equations with delay, impulsive fuzzy differential equations, fuzzy integral equations, fuzzy differential inclusions and differential inclusions with fuzzy right-hand sides with and without impulses.