Nonlinear VRFT with LASSO

TL;DR

This paper extends Virtual Reference Feedback Tuning (VRFT) to nonlinear systems by incorporating L1 regularization, addressing key issues and demonstrating the importance of regularization and dictionary selection through simple examples.

Contribution

It introduces a novel nonlinear VRFT formulation with L1 regularization and analyzes the impact of dictionary choice on controller nonlinearity representation.

Findings

L1 regularization improves nonlinear VRFT performance

Dictionary choice significantly affects controller modeling

Regularization and dictionary selection are critical for nonlinear VRFT

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 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.