Geometry of Non-linear Control Systems

Robert B. Gardner, University of North Carolina and MSRI

A report on control structures which are the generalization to manifolds of non-linear control systems.This will include a discussion of the local realization of control structures as control systems, and the universal control structure on a manifold and its classifying maps. The report will stress how the method of equivalence influenced the definition of control structure, and the interplay with the problem of determining feedback equivalence between systems. Finally this will be tied in with the recent appearance of classical geometries in the feedback classification problem.