Regularization strategies for nonparametric system identification

In the recent years several regularization strategies have been proposed to tackle linear system identification problems. One line of work has concentrated on designing and studying the properties of several Kernels for l₂-type regularization in impulse response estimation; a second stream of work has proposed using Nuclear Norm type of penalties on certain Hankel data matrices, aiming at favoring (almost) low rank solutions in subspace type procedures. The goal of this paper is twofold: (i) bring all these ideas under a common umbrella also proposing an algorithm which combines different penalties and (ii) provide a first comparison between different approaches.