Optimal interval enclosures for fractionally-linear functions, and their application to intelligent control

One of the nmin png,~lems ,ff interval computations is, given a functhm f ( x l . . . . . xn) and n intervals x i , . . . , x n , to compute the range y = f ( x l ~ , . . . , x n ) . This problem is feasible for linear fttnction s f , but for genetic Ixdynomials, it is known to be cmHputationally intractable. Becau~ of that, traditional interval techniques usually compute the e~wJa~,re ,ff y , i.e.. an interval that comains y . The chaser this enck)sure to y , the better. It is desirable to describe eases in which we can compute the op~h~ud, ~w.h~ure, i.e., the range itself. In this paper, we describe a feasible algorithm for computing the opdmal enchxsure for frcu:tiomdly thaw functi~ms f . Applkadons of this result to h~,th'gem r~#rol are described.