A mathematical representation of multi-resolutional world modeling

Abstract

Multi-resolutional representation of systems is an integral part of most hierarchical intelligent control architectures. Although many aspects of this representation have been discussed, there had been very little attempt to describe it formally. This document attempts to provide the most common aspects of a multi-resolutional representation in a general mathematical framework. The framework is described by utilizing the most abstract notions possible in an effort to cover a broad range of applications.