Interval Mathematics for Analysis of Multiresolutional Systems

The more complex the problem, the more complex the system necessary for solving this problem. For very complex problems, it is no longer possible to design the corresponding system on a single resolution level, it becomes necessary to have multiresolutional systems. When analyzing such systems -- e.g., when estimating their performance and/or their intelligence -- it is reasonable to use the multiresolutional character of these systems: first, we analyze the system on the low-resolution level, and then we sharpen the results of the low-resolution analysis by considering higher-resolution representations of the analyzed system. The analysis of the low-resolution level provides us with an approximate value of the desired performance characteristic. In order to make a definite conclusion, we need to know the accuracy of this approximation. In this paper, we describe interval mathematics -- a methodology for estimating such accuracy. The resulting interval approach is also extremely important for tessellating the space of search when searching for optimal control. We overview the corresponding theoretical results, and present several case studies