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

Xiaozhu Fang, Biqiang Mu, Tianshi Chen

TL;DR

It is shown 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.

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.

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

TL;DR

It is shown 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.

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.
Paper Structure (19 sections, 18 equations, 2 figures, 1 table)

This paper contains 19 sections, 18 equations, 2 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Background and Problem Statement
  3. CT System Identification from the Sampled Data
  4. Kernel-Based Regularization Method
  5. Problem Statement
  6. Main Result
  7. From Sampled Input Signal to CT Input Signal
  8. Closed Forms for Known Intersample and Past Behaviors
  9. ZOH and PA Input
  10. ZOH and ZA Input
  11. BL and PA Input
  12. Closed Forms for Unknown Past Behavior
  13. Simulation
  14. Data Generation
  15. Estimator Setup
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Basic setup for ZOH (left) and BL (right) inputs in applications, where $u(kT_s)$ and $y(kT_s)$ are measured, and LP Filter denotes the low-pass filter for BL conditions. Refers the more general setup to PS12.
  • Figure 2: The boxplots of FIT$_g$ (blue) and FIT$_y$ (red) for 200 MC trials. The mean and standard deviation refer to Table \ref{['ta:fit']}.