Abstract
We consider a smooth bracket-generating control-affine system in \( {\mathbb{R}^d} \) and show that any orientation-preserving diffeomorphism of \( {\mathbb{R}^d} \) can be approximated, in a very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.
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Agrachev, A.A., Caponigro, M. Dynamics control by a time-varying feedback. J Dyn Control Syst 16, 149–162 (2010). https://doi.org/10.1007/s10883-010-9087-7
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DOI: https://doi.org/10.1007/s10883-010-9087-7