Optimal synthesis problem for the fuzzy systems

Abstract

In this paper, first a space of fuzzy numbers is constructed and a scalar product is introduced. The derivative of fuzzy function in this space is defined. Further, a synthesis problem for fuzzy systems is considered. A formula for optimal control is obtained.From (20) we see that P( , s; t) is positive homogeneous on s ∈ R. It is known that [18] this function is either convex or concave with respect to s ∈ R. First, let P( , s; t) be convex. Then P( , 0; t) 1 2 [P( , −1; t)+ p( , 1; t)].