Nonlinear VRFT with LASSO

Abstract

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 theory for VRFT has been proposed early on, but its actual application requires further developments. 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 three simulation examples the critical role played in applications by two aspects: the L1 regularization and the choice of dictionary used to describe the nonlinearity of the controller.