Article

Journal of Dynamical and Control Systems

, Volume 16, Issue 2, pp 149-162

First online:

Dynamics control by a time-varying feedback

  • A. A. AgrachevAffiliated withSISSA Email author 
  • , M. CaponigroAffiliated withSISSA

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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.

Key words and phrases

Controllability discrete-time dynamics control-affine systems

2000 Mathematics Subject Classification

93B05 93C55 93B52 58A20