## Publication Date

6-1-2024

## Abstract

In many practical situations, it is desirable to select the control parameters x1, ..., xn in such a way that the resulting quantities y1, ..., ym of the system lie within desired ranges. In such situations, we usually know the general formulas describing the dependence of yi on xj, but the coefficients of these formulas are usually only known with interval uncertainty. In such a situation, we want to find the tuples for which all yi's are in the desired intervals for all possible tuples of coefficients. But what if no such parameters are possible? Since we cannot guarantee the inclusions with probability 1, a natural idea is to select parameters for which the probability that all inclusions are satisfied is the largest. To implement this idea, we need to select a probability distribution on the set of all tuples. Since we have no reason to believe that some tuples are more probable than others, it is reasonable to assume that all tuples are equally probable, i.e., that we have a uniform distribution on the set of all tuples. Interestingly, this idea leads to the same recommendation as was proposed -- based on heuristic fuzzy-logic-based arguments -- in a recent paper by Piegat. An important remaining open problem is how to efficiently compute the recommended solution.

## Comments

Technical Report: UTEP-CS-24-29