Seminar talk, 15 February 2012

Speaker: Vladimir Chetverikov

Title: Flat systems and covering over them: description and control methods

Abstract:
The talk will discuss flat control systems, i.e., the systems that are ${\mathcal {C}}$-diffeomorphic to infinite jet spaces. By analogy with the theory of differential invariants we consider finite jets of flat systems and corresponding ${\mathcal {C}}$-diffeomorphisms. We construct a map that takes every $2$-jet of ${\mathcal {C}}$-diffeomorphism to $1$-jet of flat system. This map preserves the Cartan distribution and thus lifts to a jet map of higher order. The image of $k$th prolongation consists of $(k+1)$-jets of flat systems. The analogs of differential invariants are functions constant on the image of k-th prolongation. If $k<3$ then there exists only one such function. It will be presented in the talk.

Besides, we shall show how to generalize the control methods developed for flat systems to coverings over them.