Нечеткие дифференциальные уравнения в задачах управления. Часть II

Изложены основные положения нечетких вычислений и теории нечетких обыкновенных дифференциальных уравнений. Рассмотрены различные типы решений и их взаимосвязь. Приведены разнообразные примеры решения нечетких дифференциальных уравнений первого порядка.

Fuzzy Differential Equations in Control. Part II

The initial value problem of Formulated fuzzy is obtained from a clear initial problem in which the parameters of the problem and the initial condition rely inaccurately given. This inaccuracy is modelled by fuzzy variables with triangular membership functions. Modelling by fuzzification parameters leads to fuzzy initial value problem. Depending on the type of fuzzy derivatives allocated fuzzy solutions SS (Seikkala-solution), PRS (Puri-Ralescu-solution), KFMS (Kandel-Fridman-Mingsolution) and BFS (Buckley-Feuring-solution). For the existence of BFS formulated appropriate conditions. Without proof a statement. If there SS, there BFS, however, if there BFS, it does not coincide with the SS. An algorithm for solving fuzzy initial value problem is clear in the decision of the initial problem. Then checks the conditions of existence of SS and BFS, if there is a BFS, then by fuzzification parameters clear the initial problem and finding the minimum and maximum solutions generated fuzzy BFS. If the BFS does not exist, then the SS is the solution of the corresponding system of differential equations. The examples of the simplest solutions of fuzzy initial value problems, fuzzier linear problem are solved. She appears in the calculation of fuzzy phase trajectory of a continuous system of automatic optimization remembering extremum property type nonlinearity-linearity. Figures are given representation of fuzzy numbers in the form of triangular membership functions and the equivalent of the inverse mapping. We give a list of references containing 7 items. 4 of them are in English, the other in Russian.