System Identification
System identification is concerned with estimating models of dynamical systems based on observed input and output signals. Mathematically, system identification is an inverse problem and may suffer from numerical instability. The Russian researcher Tikhonov suggested in the 1940s a general way to curb the number of solutions for inverse problems which he called regularization. A simple regularization method applied to linear regression became known as ridge regression.
Around 2000 other ideas were put forward for achieving regularization. They had links to general function estimation with mathematical foundations in Reproducing Kernel Hilbert Spaces (RKHS) and kernel techniques.
In this course, we will provide a comprehensive overview of the development of system identification. Starting from the bias-variance trade-off, we will first discuss the traditional regularized linear system identification, and move on to the kernel-based approaches. Regularization in reproducing kernel Hilbert spaces will then be described in details. Finally, we will introduce modern methods for nonlinear system identification.
Around 2000 other ideas were put forward for achieving regularization. They had links to general function estimation with mathematical foundations in Reproducing Kernel Hilbert Spaces (RKHS) and kernel techniques.
In this course, we will provide a comprehensive overview of the development of system identification. Starting from the bias-variance trade-off, we will first discuss the traditional regularized linear system identification, and move on to the kernel-based approaches. Regularization in reproducing kernel Hilbert spaces will then be described in details. Finally, we will introduce modern methods for nonlinear system identification.
Lecturer
Zeju Sun
Date
2nd April ~ 18th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 14:20 - 17:50 | A3-2-301 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
Calculus, Linear Algebra, Probability and Statistics
Syllabus
1. Introduction: Bias-Variance Trade-Off
2. Classical System Identification
3. Regularization of Linear Regression Models I
4. Regularization of Linear Regression Models II
5. Bayesian Interpretation of Regularization
6. Regularization for Linear System Identification
7. Reproducing Kernel Hilbert Spaces
8. Regularization in Reproducing Kernel Hilbert Spaces
9. Linear System Identification in RKHS
10. Nonlinear System Identification I
11. Nonlinear System Identification II
12. Numerical Experiments and Real World Applications
2. Classical System Identification
3. Regularization of Linear Regression Models I
4. Regularization of Linear Regression Models II
5. Bayesian Interpretation of Regularization
6. Regularization for Linear System Identification
7. Reproducing Kernel Hilbert Spaces
8. Regularization in Reproducing Kernel Hilbert Spaces
9. Linear System Identification in RKHS
10. Nonlinear System Identification I
11. Nonlinear System Identification II
12. Numerical Experiments and Real World Applications
Reference
[1] Pillonetto G, Chen T, Chiuso A, et al. Regularized system identification-Learning dynamic models from data[M]. Springer, 2022.
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
No
Language
Chinese
, English