A New Technique in Systems Analysis under Interval Uncertainty and Ambiguity

Abstract

The main subject of this work is mathematical and computational aspects of modeling of static systems under interval uncertainty and/or ambiguity. A cornerstone of the new approach we are advancing in the present paper is, first, the rigorous and consistent use of the logical quantifiers to characterize and distinguish different kinds of interval uncertainty that occur in the course of modeling, and, second, the systematic use of Kaucher complete interval arithmetic for the solution of problems that are minimax by their nature. As a formalization of the mathematical problem statement, concepts of generalized solution sets and AE-solution sets to an interval system of equations, inequalities, etc., are introduced. The major practical result of our paper is the development of a number of techniques for inner and outer estimation of the so-called AE-solution sets to interval systems of equations. We work out, among others, formal approach, generalized interval Gauss-Seidel iteration, generalized preconditioning and PPS-methods. Along with the general nonlinear case, the linear systems are treated more thoroughly.