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

摘要

One of the main problems of interval computations is, given a functionf(x1, ...,xn) andnintervals x1, ..., xn, to compute the range y=f(x1, ..., xn). This problem is feasible for linear functionsf, but for generic polynomials, it is known to be computationally intractable. Because of that, traditional interval techniques usually compute theenclosureof y, i.e., an interval that contains y. The closer this enclosure to y, the better. It is desirable to describe cases in which we can compute theoptimal enclosure, i.e., the range itself.