Нечеткие уравнения в частных производных в задачах управления

Рассматриваются нечеткие уравнения в частных производных первого и второго порядков и алгоритм получения для них соответствующих нечетких решений S (Seikkala) и BF (Buckley-Feuring) типов. Синтезированы нечеткие оптимальные регуляторы S и BF типов.

Fussy Partial Differential Equation in the Task of Control

Provides an overview on the use of partial differential equations in optimal control problems, it is noted that they are used in the methods of Bellman and Krasovsky Second-order equations are presented in the form of two classes: Elementary and equations whose solutions are represented as different functional series. These equations have different coefficients, which are represented as fuzzy variables. In this connection, is formed and solved one-point boundary value problem on the synthesis of fuzzy optimal control method Bellman. Next article provides basic definitions and notation of the theory of fuzzy sets, which are used for solving the fuzzy-point problem. These include the notions of membership functions; types of fuzzy numbers; fuzzy function; types of fuzzy derivatives; types of fuzzy initial value problems and algorithms for their solution. Solved fuzzy partial differential equations of the first order and second-order elementary, then we solve the problem of synthesis of fuzzy optimal linear regulator. In accordance with the types of solutions of the initial problem of fuzzy controllers are synthesized BF (Buckley-Feuring) and S (Seikkala) types. It is noted that the fuzzy equation of elliptic, hyperbolic and parabolic types are solved by numerical methods. This avoids making the fuzzy representation in the form of various types of rows. The article ends with conclusions. A reference contains 15 sources. 4 of them are foreign-source.