Old and New Challenges in Finite-Sample System Identification

Abstract

In 2005, with the publication of the LSCR algorithm (Leave-out Sign-dominant Correlation Regions), a new class of system identification algorithms, for constructing confidence regions around the unknown model parameters, was introduced. These algorithms had two characterising features that, together, set them apart from the previous literature in system identification: first, the constructed regions were accompanied by probabilistic results, certificating the inclusion of the true system parameters, that were rigorous for any number of data points, that is, results were non-asymptotic in nature; second, these inclusion results were proven under very limited prior knowledge on the noise affecting the data. In this talk, we outline a few fundamental, general ideas that are at the core of LSCR and its successors, which are known under the names of SPS (Sign-Perturbed Sums), PDMs (Perturbed Dataset Methods), and, most recently, SPCR (Sign-Perturbed Correlation Regions). In the course of the presentation, the main design and application challenges in this field will be discussed. We will also mention some recent directions of investigations in which we are directly involved; these include the relaxation of traditional assumptions such as the knowledge of the true model order, and the exploitation of a-priori knowledge on the system parameter in constructing the confidence region