Homotopy methods in control theory
Abstract
We outline a potentially transformative research program to design new tools and methods in control theory via the use of partial differential relations and h-principles. The range of applications of the methods proposed is highly relevant to the Air Force—ranging from motion planning to hybrid dynamics design to viability theory—and to the control and engineering communities at large. Partial differential relations, dened precisely herein, allow to describe and pose a very wide range of control problems in a unied language. The advantages of this new formulation are three-fold. First, it makes the geometric and topological aspects of the problem at hand apparent and allows for insights not afforded by a purely analytic formulation.We illustrate this point in the proposal. Second, it allows us to leverage deep results from geometry and topology to show existence of solutions; these results go by the name of h-principles, and we will describe a few such h-principles. Finally, it leads to the development of numerical methods; because these methods apply broadly, they can be used to solve control problems even beyond our original motivation.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010333
Entities
People
- Mohamed-Ali Belabbas
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Illinois Urbana–Champaign