Finite-Sample System Identification: An Overview and a New Correlation Method

Abstract

Finite-sample system identification algorithms can be used to build guaranteed confidence regions for unknown model parameters under mild statistical assumptions. It has been shown that in many circumstances these rigorously built regions are comparable in size and shape to those that could be built by resorting to the asymptotic theory. The latter sets are, however, not guaranteed for finite samples and can sometimes lead to misleading results. The general principles behind finite-sample methods make them virtually applicable to a large variety of even nonlinear systems. While these principles are simple enough, a rigorous treatment of the attendant technical issues makes the corresponding theory complex and not easy to access. This is believed to be one of the reasons why these methods have not yet received widespread acceptance by the identification community and this letter is meant to provide an easy access point to finite-sample system identification by presenting the fundamental ideas underlying these methods in a simplified manner. We then review three (classes of) methods that have been proposed so far-1) Leave-out Sign-dominant Correlation Regions (LSCR); 2) Sign-Perturbed Sums (SPS); 3) Perturbed Dataset Methods (PDMs). By identifying some difficulties inherent in these methods, we also propose in this letter a new sign-perturbation method based on correlation which overcome some of these difficulties.

Statistical accuracy analysis for virtual reference feedback tuning with two degrees of freedom controllers*

“…Consider those two asymptotic variance matrices cov(θ N ) and cov(η N ) obtained in above section 6 through our own mathematical derivations, the idea case is that the asymptotic variance matrix cov(θ N ) or cov(η N ) may be zero or approach to zero with N → ∞. So those two asymptotic variance matrices cov(θ N ) and cov(η N ) can measure the identification quality or testify whether our parameter estimators are efficient or asymptotic efficient (Care et al, 2018). In order to achieve the efficient or asymptotic efficient property, the asymptotic variance matrix obtained here is an important tool to consider.…”

Distribution-free uncertainty quantification for kernel methods by gradient perturbations

“…This section presents the proposed framework to quantify the uncertainty of kernel-based estimates. It is inspired by and builds on recent results from finite-sample system identification, such as the SPS and DP methods (Campi and Weyer 2005;Csáji 2016;Kolumbán 2016;Carè et al 2018). Novelties with respect to these approaches are, e.g., that our framework considers nonparametric regression and does not require the "true" function to be in the model class.…”

“…Here, we propose a non-asymptotic, distribution-free approach to quantify the uncertainty of kernel-based models, which can be used for hypothesis testing and confidence region constructions. We build on recent developments in finite-sample system identification (Campi and Weyer 2005;Carè et al 2018), more specifically, we build on the Sign-Perturbed Sums (SPS) algorithm and its generalizations, the Data Peturbation (DP) methods (Kolumbán 2016).…”

Adjustable Scaling Parameters for State of Charge Estimation for Lithium-Ion Batteries Using Iterative Multiple UKFs

“…In the model-based methods, Kalman filter-based SOC estimation methods have some advantages, such as self-correction, online computation, and complexity reduction. Kalman filter was first proposed to estimate the state of linear systems [12], and then, in order to apply it into nonlinear systems, the extended Kalman filter and unscented Kalman filter were developed [11]. Meanwhile, the date-driven methods typically include the lookup table method, matching learning-based method, artificial neural networks, and support vector machine [13].…”