 
Summary: Dynamics Control by a Timevarying Feedback
A.A. Agrachev M. Caponigro
July 24, 2009
Abstract
We consider a smooth bracket generating controlaffine system in
Rd and show that any orientation preserving diffeomorphism of Rd can
be approximated, in the very strong sense, by a diffeomorphism in
cluded in the flow generated by a timevarying feedback control which
is polynomial with respect to the state variables and trigonometric
polynomial with respect to the time variable .
1 Introduction
We consider a controlaffine system:
q = f0(q) +
m
i=1
uifi(q), q Rd
, (1)
with u = (u1, . . . , um) Rm
, where fi are smooth (i. e. C
) vector fields on
