Small-time controllability for affine systems on groups
par
Prof.Andrei Agrachev(SISSA)
→
Europe/Paris
Salle de conf. (LJAD)
Salle de conf.
LJAD
Description
We study controllability issues for left-invariant control-affine systems on the groups, including big groups like groups of diffeomorphisms or formal series. The answer is well-known systems that are linear in the control (those without drift): such a system can arbitrarily well approximate the movement in the direction of any Lie bracket polynomial of the vector fields from its right-hand side. Moreover, control functions which realize the approximations depend only on the structure of the bracket polynomials, they are the same for all systems and groups. Any Lie bracket polynomial is good in this sense. It is not true for general control-affine systems but some Lie bracket series are still good. We are going to describe a universal construction for them and give some applications.