  Virtual Reference Feedback Tuning (VRFT) is a well known and very successful
data-driven control design method. It has been initially conceived for linear
plants and this original formulation has been much explored in the literature,
besides having already found many practical applications. A nonlinear version
of VRFT has been proposed early on, but not much explored later on. In this
paper we highlight various issues involved in the application of nonlinear VRFT
and propose the inclusion of L1 regularization in its formulation. We
illustrate by means of two simple examples the critical role played by two
aspects: the L1 regularization and the choice of dictionary used to describe
the nonlinearity of the controller.
