Kernel-Based Regularized Continuous-Time System Identification from Sampled Data

TL;DR

This paper demonstrates that kernel-based regularization methods can be effectively applied to continuous-time system identification from sampled data, providing closed-form estimators for common input types and showing improved robustness and accuracy over existing methods.

Contribution

The paper introduces closed-form estimators for kernel-based regularization in CT system identification under typical sampling conditions, advancing the practical application of KRM.

Findings

The estimators have closed forms for zero-order hold and band-limited inputs.

The proposed method outperforms state-of-the-art techniques in robustness.

It achieves higher accuracy with small sample sizes.

Abstract

The identification of continuous-time (CT) systems from discrete-time (DT) input and output signals, i.e., the sampled data, has received considerable attention for half a century. The state-of-the-art methods are parametric methods and thus subject to the typical issues of parametric methods. In the last decade, a major advance in system identification is the so-called kernel-based regularization method (KRM), which is free of the issues of parametric methods. It is interesting to test the potential of KRM on CT system identification. However, very few results have been reported, mainly because the estimators have no closed forms for general CT input signals, except for some very special cases. In this paper, we show for KRM that the estimators have closed forms when the DT input signal has the typical intersample behavior, i.e., zero-order hold or band-limited, and this paves the way for the application of KRM for CT system identification. Numerical Monte Carlo simulations show that the proposed method is more robust than the state-of-the-art methods and more accurate when the sample size is small.