From vector spaces to hyperspaces, hypermaps and relations: Evolution of sets in metric spaces
Abstract
This project gathers several trails to investigate structures shared by many evolutionary systemsappearing in physics, automatics and regulation problems, economics and many other fields ofinvestigation, too many to be listed here.At this stage, only new concepts listed below have been devised and designed, and only verypreliminary results have been obtained to check their relevance. Let us mention however that theorigins of this project takes its source in set-valued analysis when differential calculus of set-valuedmaps was introduced around 1980. This new calculus allowed important advances in the eld ofcontrol theory and dierential inclusions by simplifying and generalizing the state of the art.At this point, several motivations require to go beyond vector spaces and to deal with hyperspaces(family of subsets of a space) and associate with the evolution of vectors the evolution ofthe sets to which they belong. This is the source of the recent introduction of hypermaps fromone hyperspace to another one. It requires to design a differential calculus of hypermaps and to gofrom binary relations to multinary relations". This will allow us to regulate not only vectors, butalso subsets. Operability of other concepts described below will be investigated during this threeyears project. We discuss several tractable paths opening up new avenues.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 11, 2018
- Source ID
- FA95501810254
Entities
People
- Hélène Frankowska
Organizations
- Air Force Office of Scientific Research
- National Center for Scientific Research
- United States Air Force