"Interval Analysis - Fundamentals and Electromagnetic Engineering Applications"

Interval Analysis (IA) consists of a set of rules and tools for the analysis and optimization of functions where the variables at hand are intervals of numbers and not single values as in classical arithmetical/optimization problems. For example, an interval of real values (a real interval) can be defined as a one‐dimensional compact set (a segment) b etween two extreme points, namely the minimum and maximum interval values. Also complex intervals exist and ad‐hoc rules are defined within IA for the arithmetical operations between them. Currently, the use of IA has been limited to some pioneering works in Engineering even though it has several attractive fe atures that can overcome some limitations of current state‐of‐the‐art approaches and theories. Let us consider the following issues:  IA has an intrinsic capability to deal with uncertainties, always present when experimental measurements are at hand;  analytical equations and relationships can be easily reformulated and addressed by including intervals of numbers once the fundamentals of IA are known;  the bounds of a function when evaluated over an interval are determined in a straightforward manner without the need of evaluating the function on all (infinite) points of the interval;  IA offers ad‐hoc global optimization techniques able to identify the global optimum with the desired level of accuracy. The seminar is aimed to provide an introduction to the fundamentals of Interval Analysis, starting from intuitive explanations to rigorous mathematical and methodological insights. A review of recent applications of IA in Electromagnetics will be illustrated with particular emphasis on inverse scattering pr oblems and antenna array analysis and synthesis.